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## Inequalities Worksheets

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## Compound Inequalities Worksheets

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▶ Solving One-step Inequalities

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## Unit 2: Lesson 6

- Compound inequalities: OR
- Compound inequalities: AND
- A compound inequality with no solution
- Double inequalities
- Compound inequalities examples
- Compound inequalities review
- Solving equations & inequalities: FAQ

## Compound inequalities

- (Choice A) x ≥ − 7 x\geq-7 x ≥ − 7 x, is greater than or equal to, minus, 7 A x ≥ − 7 x\geq-7 x ≥ − 7 x, is greater than or equal to, minus, 7
- (Choice B) − 7 ≤ x < 12 -7\leq x<12 − 7 ≤ x < 1 2 minus, 7, is less than or equal to, x, is less than, 12 B − 7 ≤ x < 12 -7\leq x<12 − 7 ≤ x < 1 2 minus, 7, is less than or equal to, x, is less than, 12
- (Choice C) x < 12 x<12 x < 1 2 x, is less than, 12 C x < 12 x<12 x < 1 2 x, is less than, 12
- (Choice D) There are no solutions D There are no solutions
- (Choice E) All values of x x x x are solutions E All values of x x x x are solutions

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## 7+ Compound Inequalities Worksheet For Making Math Simple and Fun

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## Solve each compound inequality and graph its solution By lyon Math

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## 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 values of x that satisfy both of the two inequalities. In other words, you want a solution set that works with both inequalities. The other way of saying it is that the solution set of the “and” compound inequality is the intersection , represented by the symbol \Large{\color{red} \cap} , of the two inequalities.
- As for the second case , it involves solving two linear inequalities joined by the word “or”. The solution of an “or” compound inequality is the set of all x that satisfy either of the two inequalities or at times satisfies the two at the same time. In other words, you want a solution that works on at least one inequality. The other way of saying it is that the solution set of the “or” compound inequality is the union , represented by the symbol \Large{\color{red} \cup } , of the two inequalities.

## The “AND” Compound Inequalities

STEP 1. Solve each inequality.

Add 1 to both sides of the inequality.

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

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

STEP 2. Graph the solutions on the number line.

STEP 3. Write the solutions in interval notation.

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

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

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

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

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

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

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

STEP 1: Solve each inequality.

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

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

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

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

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

STEP 3. Write the solution set in interval notation.

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

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

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

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

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

Here we go. Let’s work it out!

STEP 1: Solve the compound inequality.

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

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

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

## The “OR” Compound Inequalities

STEP 1. Solve each inequality.

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

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

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

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

\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 “.

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

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

\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 “.

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

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

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

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

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

It is read as ” all real numbers”.

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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

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

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.

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

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.

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.

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 ...

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

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

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

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 ...

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

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 ...

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.

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 ...

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.

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:

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.

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 ...