# 6.2: Inequalities with Addition and Subtraction

**Basic**Created by: CK-12

**Practice**Inequalities with Addition and Subtraction

Suppose your favorite baseball team had

### Guidance

**Inequalities Using Addition or Subtraction**

To solve inequalities, you need some properties.

**Addition Property of Inequality:** For all real numbers

*If* *then*

*If* *then*

The two properties above are also true for

Because subtraction can also be thought of as **“add the opposite,”** these properties also work for subtraction situations.

Just like one-step equations, the goal is to **isolate the variable,** meaning to get the variable alone on one side of the inequality symbol. To do this, you will cancel the operations using inverses.

#### Example A

*Solve for*

**Solution:** To isolate the variable

Now, check your answer. Choose a number less than 13 and substitute it into your original inequality. If you choose 0, and substitute it you get:

What happens at 13? What happens with numbers greater than 13?

#### Example B

*Solve for*

**Solution:**

The solution is shown below in a graph:

#### Example C

*Solve for x: x+23≥−13.*

**Solution:**

### Video Review

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### Guided Practice

*Solve for y: 5.6>y−3.4.*

**Solution:**

### Explore More

Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Inequalities Using Addition and Subtraction (7:48)

Solve each inequality and graph the solution on a number line.

x−1>−10 x−1≤−5 −20+a≥14 x+2<7 x+8≤−7 5+t≥34 x−5<35 15+g≥−60 x−2≤1 x−8>−20 11+q>13 x+65<100 x−32≤0 x+68≥75 16+y≤0

**Mixed Review**

- Write an equation containing (3, –6) and (–2, –2).
- Simplify:
|2−11×3|+1 . - Graph
y=−5 on a coordinate plane. y varies directly asx . Whenx=−1, y=45 . Findy whenx=163 .- Rewrite in slope-intercept form:
−2x+7y=63 .

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 6.2.

### Image Attributions

## Description

## Learning Objectives

Here you'll learn how to use addition and subtraction to find the solutions to one-step inequalities.

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## Date Created:

Feb 24, 2012## Last Modified:

Aug 20, 2015## Vocabulary

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