# Solving One-Variable Equations

## Objective

Solve and graph inequalities with variables on one side of the inequality.

## Common Core Standards

### Core Standards

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• A.REI.B.3 — Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

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• 7.EE.B.4.B

## Criteria for Success

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1. Solve inequalities with variables on one side and use substitution to check answers.
2. Accurately multiply and divide with negative coefficients in inequalities, paying close attention to the direction of the inequality symbol.
3. Graph solutions to inequalities.
4. Write, solve, and interpret solutions to inequalities for applications.

## Tips for Teachers

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Lessons 11 and 12 extend on 7.EE.4b and bridge a gap to high school standard A.REI.3. Inequalities are not included in the 8th grade standards, but this is a natural extension of students’ work with equations from earlier in the unit, especially now that students are able to work with more complex equations and inequalities. These two lessons can be treated as optional.

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## Anchor Problems

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### Problem 1

Solve the inequality. Then pick a value for $x$ and check your answer. Lastly, graph your solution on a number line.

$8-4(x-2)+6(x-1)>20$

#### Guiding Questions

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### Problem 2

Solve the inequality.

${4-{x\over3}\leq {3\over4}(32)}$

#### Guiding Questions

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### Problem 3

Noah is creating a rectangular picture frame out of wood. He wants the width of the frame to be 6 inches less than half the length. If Noah has a total of 60 inches of wood that he can use for the frame, write and solve an inequality to represent the possible measurements of the length of the frame.

#### Guiding Questions

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## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

• Include problems similar to Anchor Problems #1 and #2.

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Solve each inequality, then represent the solutions on a number line.

a.    ${{{-2x+4}\over5} \geq 18}$

b.    ${{3\over5}(10-15x)+13x > -20}$

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