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Inequalities Worksheets

Teeming with adequate practice our printable inequalities worksheets come with a host of learning takeaways like completing inequality statements, graphing inequalities on a number line, constructing inequality statements from the graph, solving different types of inequalities, graphing the solutions using appropriate rules and much more for students in grade 6 through high school. Solutions to inequalities are infinite and are presented as an interval. Kick-start practice with our free inequalities worksheets!

» Translating Inequality Phrases

» Compound Inequalities

» One Step Inequalities

» Graphing Linear Inequalities

» Two Step Inequalities

» Absolute Value Inequalities

» Multi Step Inequalities

» Quadratic Inequalities

Completing Inequality Statements

Completing Inequality Statements

Tackle this batch of printable inequalities worksheets by plugging each of the four options in the inequality statement. Grade 6 students circle all the possible values that make the inequality statement true.

pdf 1

Graphing Inequalities on a Number Line

Graph the inequality on a number line by drawing a circle over the number. Fill it if the inequality has a ≥ or ≤, leave it unfilled if it has a > or <. Draw a line toward the right, if the solutions are greater than the number and toward the left if they are less.

easy 1

Writing Inequalities from Number Lines

Study the graph, and construct the inequality that best describes it. Grade 7 students look for open and closed circles, watch for the direction of the line and build an inclusive or strict greater than or less than inequality in no time.

practice 1

Identifying the Solution Graph

If buffing up skills in solving and graphing inequalities is on your mind, then these printable inequalities worksheets should be your obvious choice. Students choose the graph that best describes the solution for each single variable inequality.

worksheet 1

Identifying Inequalities from Number Lines

Observe the graph in these pdfs keenly and construct an inclusive inequality with a closed circle or a strict one with an open circle. Students in 7th grade and 8th grade use < if the line extends toward the right and > for a line stretching toward the left.

exercise 1

Identifying Solutions in Interval Notations

Draw logical conclusions, whether the interval with a bracket or parentheses is the right solution to the inequality. The task in these pdfs for grade 8 and high school students is to choose the correct interval notation that best describes each inequality.

Translating Inequality Phrases Worksheets

Translating Inequality Phrases Worksheets

Primarily focusing on reading phrases and converting them into algebraic inequalities, these printable worksheets are sure to give students an insight into comprehending inequalities and their real-life connection.

(12 Worksheets)

One Step Inequalities Worksheets

One Step Inequalities Worksheets

Are you looking for a variety of exercises to introduce or recapitulate one-step inequalities? Then be assured you are in the right place. With a host of pdfs for your 6th grade students to choose from, there'll be no dearth of practice material.

(51 Worksheets)

Two Step Inequalities Worksheets

Two Step Inequalities Worksheets

Refine your skills in solving and graphing inequalities in two simple steps. Grade 7 students separate the like terms on either side of the inequality. Use inverse operations to isolate the variable and solving the inequality will be duck soup.

Multi Step Inequalities Worksheets

Multi Step Inequalities Worksheets

Work methodically toward solving and graphing the multi-step inequalities. With the adequate practice provided in these worksheets finding solutions to multi-step inequalities will no longer be a hard nut to crack for your students in grade 8.

(45 Worksheets)

Compound Inequalities Worksheets

Compound Inequalities Worksheets

Whether you are looking for inequalities that are joined together by the conjunction "and" or "or", these worksheets on inequalities beef up practice and prepare high school students in solving and graphing such inequalities.

Graphing Linear Inequalities Worksheets

Graphing Linear Inequalities Worksheets

Visualize the inequality on a graph, analyze the properties of the line, observe the graph and figure out the inequality, sketch the inequality graph are some exercises present here to challenge your high school students.

(24 Worksheets)

Absolute Value Inequalities Worksheets

Absolute Value Inequalities Worksheets

What happens when two important concepts absolute value and inequalities merge? They create an interesting topic absolute value inequalities. Surge ahead in solving the absolute value inequalities featured in our printable inequalities worksheets.

Quadratic Inequalities Worksheets

Quadratic Inequalities Worksheets

Inequalities involving the second degree taking precedence in these pdfs. Solve the quadratic inequalities, find the intervals that make the inequality true, graph the inequality by sketching the parabola are some exercises included here.

(18 Worksheets)

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Inequalities Worksheets

The pages below all have printable algebra worksheets for teaching students to solve and graph inequalities. Topics include basic single-variable inequalities, as well as, one-step, two-step, and compound inequalities.

Inequalities Worksheets

Introduction to inequalities. Solve and graph the inequalities with only one variable. Students graph the inequality. They do not need to perform any steps to isolate the variable. (example: a ≥ 7)

These inequality worksheets have one variable in each problem. Students need to isolate the variable using only one step. (example: 12 - x ≤ 8)

This page has very basic worksheets to help students identify dependent and independent variables, evaluate algebraic expressions and solve for variables in equations.

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Compound Inequalities Worksheets

A compound inequality is one that consists of two inequalities joined with the words “and” or “or”. The compound inequality with “and” represents an intersection and the inequality with “or” represents a union. Compound inequalities with “and” indicate that both the statements are true and the solutions are same as well. The graphs of such inequalities overlap. Compound inequalities with “or” indicate that either of the expression is true. Solve the inequalities featured in these printable compound inequalities worksheets using the basic steps of isolating the variables by applying the additive or multiplicative inverse.

These pdf worksheets are curated for students of grade 8 and above.

Solving Compound Inequalities

Related Worksheets

▶ Solving One-step Inequalities

▶ Solving Two-step Inequalities

▶ Solving Multi-step Inequalities

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Unit 2: Lesson 6

Compound inequalities

Algebra 2 Worksheets

Equations and inequalities worksheets.

Here is a graphic preview for all of the Equations and Inequalities Worksheets. You can select different variables to customize these Equations and Inequalities Worksheets for your needs. These Equations and Inequalities Worksheets are randomly created and will never repeat so you have an endless supply of quality Equations and Inequalities Worksheets to use in the classroom or at home. Our Equations and Inequalities Worksheets are free to download, easy to use, and very flexible.

These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Click here for a Detailed Description of all the Equations and Inequalities Worksheets .

Quick Link for All Equations and Inequalities Worksheets

Click the image to be taken to that Equations and Inequalities Worksheets.

Detailed Description for All Equations and Inequalities Worksheets

Multiple Step Equations with Integers Worksheets These Equations and Inequalities Worksheets will produce multiple step problems containing integers. These worksheets will produce ten problems per worksheet. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Multiple Step Equations with Decimals Worksheets These Equations and Inequalities Worksheets will produce multiple step problems containing decimals. These worksheets will produce ten problems per worksheet. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Absolute Value Equations Worksheets These Equations and Inequalities Worksheets will produce absolute value problems with monomials and polynomials expressions. These worksheets will produce ten problems per worksheet. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Distance, Rate, and Time Word Problems These Equations and Inequalities Worksheets will produce distance, rate, and time word problems with ten problems per worksheet. You may select the numbers to be represented with digits or in words. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Mixture Word Problems These Equations and Inequalities Worksheets will produce mixtures word problems with ten problems per worksheet. You may select the numbers to be represented with digits or in words. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Work Word Problems These Equations and Inequalities Worksheets will produce work word problems with ten problems per worksheet. You may select the numbers to be represented with digits or in words. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Multiple Step Inequalities Worksheets These Equations and Inequalities Worksheets will produce multiple step inequalities problems for graphing. You may select which type of inequality to use in the problems. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Compound Inequalities Worksheets These Equations and Inequalities Worksheets will produce compound inequalities problems for graphing. You may select which type of inequality to use in the problems. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Absolute Value Inequalities Worksheets These Equations and Inequalities Worksheets will produce absolute value inequalities problems for graphing. You may select which type of inequality to use in the problems. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade.

Compound Inequalities Worksheets

Inequalities come in as a new territory to explore as so far we have always tried to get an answer. In contrary to the general notion of getting one answer, solving compound inequalities might end up at getting one, more, or no answers at all. Multiple answers mostly come as a range but it should not come as a surprise as all those values hold true for the given inequality.

Benefits of Worksheet on Compound Inequalities

When you are doing compound inequalities worksheets, you become fluent with the process. In order to solve an inequality, you need to perform a certain number of arithmetic operations and in the beginning, it might appear as cumbersome. Solving a few questions would make it easier for you to face and solve the question when it actually comes in front of you. It will help you get an edge over the rest of the students.

Download Compound Inequalities Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

Home » Worksheets » 7+ Compound Inequalities Worksheet For Making Math Simple and Fun

inequalities compound worksheet

7+ Compound Inequalities Worksheet For Making Math Simple and Fun

Stop your search! We have compiled a collection of quality compound inequalities worksheets that are perfect to assist students in obtaining the skills they need to solve these problems and move up to the next level.

Things to look for when choosing a compound inequalities worksheet

As a math teacher, it is imperative that your students learn to solve compound inequalities. It will prove beneficial for them during their high school and college mathematics courses going forward.

When choosing worksheets for your students to complete, make sure there is ample space for them to graphically demonstrate their solutions. For equations such as compound inequalities, to draw multiple number lines with markers. In the beginning, worksheets with worked examples help students get started when they are out of the classroom.

Best Compound Inequalities Worksheet

Introduction to compound inequalities by live worksheets.

inequalities compound worksheet

This is a free interactive worksheet from Live Worksheets, but it can also be printed as a handout. It is designed as an guided lesson and starts with simple inequalities. Gradually it builds up into compound inequalities. An answer key is available.

Solve each compound inequality and graph its solution By lyon Math

inequalities compound worksheet

This worksheet from Mrs. Lyon’s math blog has plenty of white space for students to draw number lines and work out their answers. Students will need to combine terms and solve each variable before graphing.

Compound Inequalities Worksheets By Math Monks

inequalities compound worksheet

Math Monks has 4 compound inequalities worksheets that become progressively more difficult. The worksheets are free, but you will have to navigate a pop up advertisement (click Close when the ad appears) to print the page. It does not include an answer key.

Compound Inequalities Worksheets By Tutoring Hour

inequalities compound worksheet

Tutoring Hour has several practical worksheets available for free download on their website. The handouts are clean and simple with moderate space for students to show their work. Aside from this worksheet, there are two others for practice on compound inequalities. They do not include an answer key.

Compound Inequalities Worksheet with Lots of White Space

inequalities compound worksheet

This free worksheet has limitations, but it is beautifully spaced with enough room for students to show their work. It’s perfect for middle school classrooms where students haven’t mastered small handwriting. It’s also one of the few compound inequality worksheets has contains word problems. The problem numbering is slightly off. The original worksheet was scanned awkwardly. There is a handwritten answer key.

Write the Compound Inequality Represented by the Graph (Including Special Cases) By School Wires

inequalities compound worksheet

This is a scanned worksheet available for free  on School Wire. Instead of graphing the inequality, students have to determine the compound inequality shown on the graph . The worksheet also contains word problems. It includes special cases. An answer key is available.

Compound Inequalities Customizable Worksheet By Math Aid

inequalities compound worksheet

Math Aid offers free (if you are okay with flashing ads) worksheets. Each worksheet can be customized by difficulty, number of problems, and language. Answer keys are included.

Where to find compound inequalities worksheets online

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Solving Compound Inequalities

When solving compound inequalities, we are going to deal with two general cases or types.

In both cases, the solutions of compound inequalities can be expressed as graphs on the number line and also as interval notations.

I suggest that you first graph the solutions of the two inequalities on the number line before writing the solution of the compound inequality in the interval notation. By having a visual representation of how the two inequalities behave on the number line, it is much easier to write its corresponding interval notation.

We will also go over some examples where the compound inequality has no solution or infinite solution.

Somewhere in our examples, we will discuss an “and” compound inequality case which can be condensed into a single inequality with three parts: left side, middle part, and right side. An example would be - 1 \le x \le 3 which is derived from -1 \le x and x \le 3 . By writing it in this form, it can allow us to solve the compound inequality much quicker.

The “AND” Compound Inequalities

Solve the compound “and” inequality by solving each of the two inequalities separately then examine or consider their solutions altogether. For the “and” case, we want to find all the numbers or values that can make both the two inequalities true .

Example 1: Solve the compound inequality x - 1 > 1 and 27 \ge 2x - 1 . Graph the solutions on the number line. Then, write your solutions in interval notation.

STEP 1. Solve each inequality.

Add 1 to both sides of the inequality.

x - 1 > 1

x - 1+1 > 1+1

\color{red}x > 2

Add both sides of the inequality by 1 then divide by 2 . Finally, make sure that the variable is on the left side. When you swap location, in this case, the variable x will move from right to left. The relative orientation of the inequality symbol should remain the same to keep the meaning unchanged. One way to think about it is that the “mouth” of the inequality symbol is opening towards the number 14 . So when you swap, the “mouth” of the inequality must still be pointing towards 14 .

27 \ge 2x - 1

27 + 1 \ge 2x - 1 + 1

{\Large{{{28} \over 2}}} \ge {\Large{{{2x} \over 2}}}

\color{red}x \le 14

The solutions are given by \color{red}x > 2 and \color{red}x \le 14 .

STEP 2. Graph the solutions on the number line.

For \color{red}x > 2 , the point 2 is not included as part of the solutions since x > 2 means all numbers greater than 2 . In addition, it does not have any conditions of equality that’s why we must exclude the number 2 . So we will put an open circle over 2 to indicate that it is not a solution. The solutions are all numbers greater than 2 , thus we draw an arrow to the right of 2 .

For \color{red}x \le 14 , we read it as “ x is less than or equal to 14 “. Notice there is a condition of equality, therefore the number 14 is part of the solution so we will put a closed circle over it. All numbers to the left of 14 are also solutions so we will draw an arrow pointing to the left of it.

The final solutions will be the intersection or overlap of the two inequalities: \color{red}x > 2 and \color{red}x \le 14 . Notice that all the numbers between 2 and 14 intersect so they are part of the final solutions of the “and” compound inequality. They also intersect at the number 14 so we add it in the solution set. However, they do not intersect at point 2 , thus we drop it off as part of the solutions. We have just figured out the complete solution set of the given compound inequality.

the compound inequality is graphed on the number line: all values of x greater than 2 but less than or equal to 14

STEP 3. Write the solutions in interval notation.

Observe that all numbers between 2 and 14 are part of the solutions. In addition, the number 2 is excluded because it is with an open circle while 14 is included because it is covered with a closed circle . Now, we use a rounded bracket or parenthesis if it is excluded (2 is excluded), and use a square bracket if included (14 is included).

\Large{\left( {2,14} \right]}

It is read as “all the numbers greater than 2 but less than or equal to 14 “.

Don't forget

Remember: This type of interval is also known as half-closed or half-open interval because one of the two endpoints is included but the other is not.

Example 2: Solve the compound inequality 2 + 3x > - 10 and 2\left( {x - 1} \right) < x + 4 . Graph the solution set on the number line. Then, write the solution set in the interval notation.

Subtract both sides of the inequality by 2 . Then divide both sides by 3 .

2 + 3x > - 10

2 - 2 + 3x > - 10 - 2

3x > - 12

{\Large{{{3x} \over 3}}} > {\Large{{{ - 12} \over 3}}}

\color{red}x > - \,4

Distribute the 2 to the binomial inside the parenthesis. Add 2 on both sides by of the inequality. Then subtract both sides by x .

2\left( {x - 1} \right) < x + 4

2x - 2 < x + 4

2x - 2 + 2 < x + 4 + 2

2x < x + 6

2x - x < x - x + 6

\color{red}x < 6

The solutions are given by \color{red}x > - \,4 and \color{red}x < 6 .

STEP 2. Graph the solution set on the number line.

A strict inequality is a type of inequality that is either absolutely greater than a number, x>a , or absolutely less than a number, x<a . Notice that strict inequality does not contain any equality component.

On the other hand, the inequality symbol x \ge a which is read as “ x is greater than or equal to a and the inequality symbol x \le a which is read as “ x is less than or equal to a ” are both non-strict inequalities because they have the equality conditions.

The inequality \color{red}x > - \,4 is a strict inequality therefore we will put an open circle over -4 as it is not part of the solutions, and draw an arrow to the right. Similarly, \color{red}x < 6 is a strict inequality thus we will put an open circle over 6 , and draw an arrow to the left.

The final solution set will be the intersection of \color{red}x > - \,4 and \color{red}x < 6 which are all the numbers between -4 and 6 but excluding the endpoints -4 and 6 .

the compound inequality is graphed on the number line: all values of x between -4 and 6

We will use rounded brackets or parentheses on both sides to signify that both endpoints are excluded from the solution set.

\Large{\left( {-4,6} \right)}

It is read as “all the numbers greater than -4 but less than 6 “.

Don't forget

Remember: This type of interval is also known as an open interval because the two endpoints are excluded in the solution set. That is, they are NOT part of the solutions.

Example 3: Solve the compound inequality 5 - 3\left( {x - 2} \right) \le x - \left( { - 2x + 13} \right) and 5 - \left( {x + 1} \right) \le 2\left( {7 - x} \right) + 1 . Graph the solution set then write its solutions in the interval notation.

STEP 1: Solve each inequality.

Get rid of the parenthesis on each side of the inequality using the Distributive Property of Multiplication over Addition. Add 5 and 6 on the left. Subtract both sides by 11 . Subtract both sides by 3x . To solve x , divide both sides by -6 . Since we divide each side by a negative number, we will switch the direction of the inequality. That is, “from less than or equal to” to “greater than or equal to”.

5 - 3\left( {x - 2} \right) \le x - \left( { - 2x + 13} \right)

5 - 3x + 6 \le x + 2x - 13 

- 3x + 11 \le 3x - 13  

- 3x + 11 - 11 \le 3x - 13 - 11

- 3x \le 3x - 24 

- 3x -3x \le 3x - 3x+24 

- 6x \le-24

{\Large{{{ - 6x} \over { - 6}}}} \le {\Large{{{ - 24} \over { - 6}}}}

\color{red}x \ge 4

Eliminate the parentheses using the Distributive Property of Multiplication over Addition. Subtract 5 by 1 on the left side. Subtract 4 to both sides of the inequality. Then add 2x to both sides to finish it off.

5 - \left( {x + 1} \right) \le 2\left( {7 - x} \right) + 1

5 - x - 1 \le 14 - 2x + 1 

4 - x \le 15 - 2x 

4 - 4 - x \le 15 - 4 - 2x 

- x \le 11 - 2x 

- x + 2x \le 11 - 2x + 2x

\color{red}x \le 11

The solutions are given by \color{red}x \ge 4 and \color{red}x \le 11 .

For \color{red}x \ge 4 , we will shade the circle above 4 to show that it is included in the solutions because the inequality has a condition of equality, that is, “greater than or equal to”. The arrow points to the right of 4 because it has a component of “greater than”.

For \color{red}x \le 11 , we will also shade the circle above 11 to indicate that is it is part of the solution set since the inequality has a condition of equality, that is, “less than or equal to”. The arrow points to the left of 11 because it is of the case of less than.

As for the final solution set, we find all the points where the two inequalities intersect. Obviously, they intersect between 4 and 11 . More so, they also overlap at the endpoints. Therefore, the final solution set contains all the points between the endpoints 4 and 11 and including the endpoints.

x is between 4 and 11 and including the endpoints 4 and 11

STEP 3.  Write the solution set in interval notation.

We will use square brackets on both sides to signify that both endpoints are included in the solution set.

\Large{\left[ {4,11} \right]}

It is read as “all numbers greater than or equal to 4 but less than or equal to 11 “.

an elephant

Remember: This type of interval is also known as a closed interval because the two endpoints are included in the solution set. That is, they are part of the solutions.

Example 4: Solve the compound inequality 3x - 2\left( {1 - x} \right) < x - 6 and 10 - x < x + 2 . Graph the solution set then write its solutions in the interval notation.

Distribute the -2 into the binomial 1-x on the left side of the inequality to remove the parenthesis. Add 3x and 2x on the left side as well. Add 2 to both sides of the inequality. Subtract x on both sides. Finally, divide both sides of the inequality by 4 .

3x - 2\left( {1 - x} \right) < x - 6

3x - 2 + 2x < x - 6

5x - 2 < x - 6

5x - 2 + 2 < x - 6 + 2

5x < x - 4

5x - x < x - x - 4

4x <  - 4

{\Large{{{4x} \over 4}}} < {\Large{{{ - 4} \over 4}}}

\color{red}x <- 1

Subtract both sides of the inequality by 10 . Then, subtract it also on both sides by x . Finally, divide each side by -2 . Since we are dividing by a negative number, we must flip or switch the direction of the inequality symbol. In this case, from less than to greater than.

10 - x < x + 2

10 - 10 - x < x + 2 - 10

- x < x - 8

- x - x < x - x - 8

- 2x <  - 8

{\Large{{{ - 2x} \over { - 2}}}} > {\Large{{{ - 8} \over { - 2}}}}

\color{red} x > 4

Observe that the solutions of the two inequalities \color{red}x <- 1 and \color{red} x > 4 do not intersect, and thus the compound inequality has no solution .

It is more obvious that they don’t overlap if we look at their graphs on the number line.

no solution

Example 5: Solve the compound inequality - 5 < 3x + 7 \le 22 . Graph the solution set then write its solutions in the interval notation.

This hybrid-looking inequality which is comprised of two inequality symbols and three parts is actually a combination of two inequalities joined together by an “AND” conjunction.

We can separate this compound inequality into two inequalities with an “AND” connector and then solve them as usual. This is how it looks if we break the compound inequality into two simpler inequalities.

-5 is less than 3x +7 and 3x+7 is less than or equal to 22

However, there is no need to separate it into two inequalities. We can solve the compound inequality as it stands. In fact, I like it the way it is because it is much easier to solve.

The goal is to isolate the variable of the middle part. To keep everything balanced, whatever we do on the middle part, we must do the same on the left side and the right side. When it is done properly, the answer should come out nicely!

Here we go. Let’s work it out!

STEP 1: Solve the compound inequality.

To solve for x , we subtract the middle by 7 which means we have to do the same with the left and right side of the compound inequality. Finally, to isolate x , we divide the middle by 3 which we will do the same to the left and right.

- 5 < 3x + 7 \le 22

- 5 {\color{red}- 7} < 3x + 7{\color{red} - 7} \le 22{\color{red} - 7} 

- 12 < 3x \le 15

{\Large{{{ - 15} \over {\color{red}3}}}} < {\Large{{{3x} \over {\color{red}3}}}} \le {\Large{{{15} \over {\color{red}3}}}}

- 4 < x \le 5

The solutions are given by - 4 < x \le 5 .

x is between -4 and 5 but 5 is included in the solution

\Large{\left( {-4,5} \right]}

It is read as “all numbers greater than -4 but less than or equal to 5 “.

The “OR” Compound Inequalities

Solve the compound “or” inequality by solving each of the two inequalities separately. For the “or” case, we want to find all the numbers that can make at least one of the two inequalities to be true .

remember all compound inequalities below deal with the OR case

Example 6: Solve the compound inequality 2x - 5 > 3x + 2 or x - 1 < 2x - 5 . Graph the solutions on the number line. Then, write your solutions in interval notation.

STEP 1.  Solve each inequality.

Add 5 to both sides of the inequality. Then subtract 3x on both sides. Finally, divide -1 on both sides. Don’t forget to flip the inequality symbol because we divided a number by a negative number.

2x - 5 > 3x + 2

2x - 5 + 5 > 3x + 2 + 5

2x > 3x + 7

2x - 3x > 3x - 3x + 7

{\Large{{{ - x} \over { - 1}}}} < {\Large{{7 \over { - 1}}}}

\color{red}x < - 7

Add both sides by 1 . Then subtract by 2x to both sides. Divide both sides of the inequality by -1 thus switching the direction of the inequality symbol.

x - 1 < 2x - 5

x - 1 + 1 < 2x - 5 + 1

x < 2x - 4

x - 2x < 2x - 2x - 4

- x < - 4

{\Large{{{ - x} \over { - 1}}}} > {\Large{{4 \over { - 1}}}}

\color{red}x > 4

The solutions are given by \color{red}x < - 7 or \color{red}x > 4 .

STEP 2.  Graph the solution set on the number line.

x is less than -7 or x greater than 4

\left( { - \infty ,7} \right) \cup \left( {4,\infty } \right)

It is as read as “all numbers less than negative 7 or all numbers greater than 4 “.

Example 7: Solve the compound inequality 2\left( {x + 1} \right) \le x - 2 or 3\left( {x - 1} \right) \le 4x - 3 . Graph the solutions on the number line. Then, write your solutions in interval notation.

Distribute 2 into the quantity (x+1). Subtract 2 on both sides of the inequality. Finally, subtract x on both sides to get to the final solution.

x is less than or equal to -4

Distribute 3 into the quantity (x-1). Next, add 3 to both sides of the inequality. Then, subtract sides by 4x . Finally divide both sides by -1 . Please don’t forget to switch the direction of the inequality from “less than or equal to” to “greater or equal to”.

x is greater than or equal to 0

The solutions are given by \color{red}x \le - 4 or \color{red}x \ge 0 .

x is less than or equal to -4 or x is greater than or equal to 0

\left( { - \infty , - 4} \right) \cup \left( {0,\infty } \right)

It is read as “all numbers less than or equal to -4 or all numbers greater than or equal to 0 “.

Example 8: Solve the compound inequality 2\left( {x + 1} \right) - 3\left( {x + 1} \right) < 0 or 4x + 3 \ge 15 + 6x . Graph the solution set on the number line. Then, write the solution set in the interval notation.

Apply the Distributive Property of Multiplication over Addition twice on the left of the inequality. Combine similar terms. Add 1 on both sides. Finally divide both sides of the inequality by -1 . Don’t forget to switch the direction of the opening of the inequality symbol since we have divided by a negative number.

x is greater than -1

Subtract 3 on both sides, followed by subtracting 6x . Divide each side by -2 then flip the direction of the inequality.

x is less than or equal to -6

The solutions are given by \color{red}x > - 1 or \color{red}x \le - 6 .

x is less than or equal to negative 6 or x is greater than or equal to negative 1

\left( { - \infty , - 6} \right] \cup \left( { - 1,\infty } \right)

It is read as “all numbers less than or equal to -6 or all numbers greater than or equal to -1 “.

Example 9: Solve the compound inequality 0 < 3 - \left( {x + 4} \right) or 2 < 1 - \left( {x - 2} \right) . Graph the solution set on the number line. Then, write the solution set in the interval notation.

Apply the Distributive Property on the right side of the inequality then add x to both sides of the inequality.

x is less than -1

Apply the Distributive Property on the right side then add x to both sides of the inequality. Finally, subtract 2 on both sides to get to the final answer.

x is less than 1

The solutions are given by \color{red}x < - 1 or \color{red}x < 1 .

x is less than 1

\left( { - \infty ,1} \right)

It is read as “all numbers less than 1 “.

Example 10: Solve the compound inequality 10x - 8 < 7x + 7 or 3x - 2\left( {2 - x} \right) \ge 1 . Graph the solution set on the number line. Then, write the solution set in the interval notation.

Add 8 to both sides. Next, subtract 7x on both sides. Finally, divide both sides by positive 3 .

x is less than 5

Apply the distributive property on the left side. Combine similar terms. Add 4 one both sides. Finally, divide positive 5 on both sides.

x is greater than or equal to 1

The solutions are given by \color{red}x < 5 or \color{red}x \ge 1 .

all real numbers

\left( { - \infty ,\infty } \right)

It is read as ” all real numbers”.

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  1. PDF Solve each compound inequality and graph its solution.

    Compound Inequalities Date_____ Period____ Solve each compound inequality and graph its solution. 1) m or ... Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. Title: Compound Inequalities.ks-ia1 Author: Mike

  2. Compound Inequalities Worksheets

    Decompose each compound inequality in these printable worksheets into two linear inequalities. Direct 8th grade students to solve them individually in one, two, or multi-steps and select the option that best describes the solution. One-Step Two-Step Multi-Step Identifying Graphical Solutions

  3. Compound inequalities review (article)

    This compound inequality is true for values that are both greater than zero and less than four. Graphically, we represent it like this: So, in this case, 2 2 is a solution of the compound inequality, but 5 5 is not because it only satisfies one of the inequalities, not both.

  4. Inequalities Worksheets

    Compound Inequalities Worksheets Whether you are looking for inequalities that are joined together by the conjunction "and" or "or", these worksheets on inequalities beef up practice and prepare high school students in solving and graphing such inequalities. (51 Worksheets) Graphing Linear Inequalities Worksheets

  5. 2.7: Solve Compound Inequalities

    A compound inequality is made up of two inequalities connected by the word "and" or the word "or." To solve a compound inequality means to find all values of the variable that make the compound inequality a true statement. We solve compound inequalities using the same techniques we used to solve linear inequalities.

  6. Inequalities Worksheets

    The pages below all have printable algebra worksheets for teaching students to solve and graph inequalities. Topics include basic single-variable inequalities, as well as, one-step, two-step, and compound inequalities. Introduction to inequalities. Solve and graph the inequalities with only one variable. Students graph the inequality.

  7. PDF Infinite Algebra 1

    Worksheet by Kuta Software LLC Algebra 1 Compound Inequalities Name_____ ©R n2g0d1C5c VKNuotLaS _SMoyfJt[wHadrPey rLeLjCk.B b VAvlNlv drWiogdhgtBsG Frlejs_ejrvvgevd_.-1-EXAMPLES: Solve each compound inequality and graph its solution. 1) 5 - 3n > -10 or 5n - 5 ³ 352) -9k + 7 ³ 16 and 5 - k £ 13 ...

  8. Compound Inequalities Worksheets

    Solve the inequalities featured in these printable compound inequalities worksheets using the basic steps of isolating the variables by applying the additive or multiplicative inverse. These pdf worksheets are curated for students of grade 8 and above. Related Worksheets Solving One-step Inequalities Solving Two-step Inequalities

  9. Compound inequalities

    Compound inequalities | Algebra (practice) | Khan Academy Math > Algebra 1 > > Compound inequalities You might need: Calculator Solve for x x. -7x-50\leq -1\quad \maroonC {\text { AND}} \quad -6x+70>-2 −7x − 50 ≤ −1 AND − 6x +70 > −2 Choose 1 answer: x\geq-7 x ≥ −7 A x\geq-7 x ≥ −7 -7\leq x<12 −7 ≤ x < 12 B -7\leq x<12 −7 ≤ x < 12 x<12 x < 12 C

  10. PDF Solve Compound Inequalities

    Solve each compound inequality and graph its solution. 19) − w<− { or 𝑥 5 > u 20) − v< s t+ =< t t 21) s t < t v or n 9 R s u 22) + {R s w and x 6 Q v 23) − z Q m t < w 24) + x R s { or r 3 <− x. Math Worksheets Name: _____ Date: _____ … So Much More Online! Please visit: www.EffortlessMath.com Answers Compound Inequalities

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    The Inequalities Worksheets are randomly created and will never repeat so you have an endless supply of quality Inequalities Worksheets to use in the classroom or at home. We have properties of inequality handout, graphing single variables, one step by adding, subtracting, multiplying, and dividing, two step, multiple step, compound, and ...

  12. Algebra 2 Worksheets

    These Equations and Inequalities Worksheets will produce multiple step inequalities problems for graphing. You may select which type of inequality to use in the problems. These Equations and Inequalities Worksheets are a good resource for students in the 8th Grade through the 12th Grade. Compound Inequalities Worksheets

  13. Compound Inequalities Worksheets

    Benefits of Worksheet on Compound Inequalities. When you are doing compound inequalities worksheets, you become fluent with the process. In order to solve an inequality, you need to perform a certain number of arithmetic operations and in the beginning, it might appear as cumbersome. Solving a few questions would make it easier for you to face ...

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    Compound Inequalities Worksheets By Math Monks Math Monks has 4 compound inequalities worksheets that become progressively more difficult. The worksheets are free, but you will have to navigate a pop up advertisement (click Close when the ad appears) to print the page. It does not include an answer key. Find It Here

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    Finding slope from two points. Finding slope from an equation. Graphing lines using slope-intercept form. Graphing lines using standard form. Writing linear equations. Graphing linear inequalities. Graphing absolute value equations. Direct variation. Systems of Equations and Inequalities.

  17. Solving Compound Inequalities

    Worksheets; New; Solving Compound Inequalities. When solving compound inequalities, we are going to deal with two general cases or types. The first case involves solving two linear inequalities joined by the word "and". The word "and" is also known as a conjunction. The solution of an "and" compound inequality is the set of all ...

  18. Compound Inequality Worksheet Teaching Resources

    This compound inequalities worksheet resource is a great way for students to master their skills through practice. With the self-checking Google Sheets students receive instant feedback on their work! Compound inequality practice is key in master; therefore, there are a variety of questions that include fractions.

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    Compound Inequality Worksheets. Compound Inequality Worksheets. Title: Solve each inequality and graph the solution. Level: Level 1: Medium. Rows: 6 4 5 7 8. Columns:

  20. Compound Inequalities (with Solutions)

    Three worksheets at different difficulty levels (First Steps, Strengthen and Extend). The questions are carefully selected so that they help students to develop their understanding of inequalities that have both an upper and lower bound. The Extend activity requires students to combine two different inequalities into one. Solutions are included.

  21. Compound Inequalities Foldab;e Teaching Resources

    A compound inequality contains at least two inequalities separated by "and" or "or." Understanding this skill builds a student's ability to think logically and to read, use, and develop Venn Diagrams. ... *3-day lesson *warmups/exit tickets *vocabulary *practice problems *9 student pages/ worksheet Day 1: -identify inequality signs -interpret ...