# 6.2: Inequalities with Addition and Subtraction

**Basic**Created by: CK-12

**Practice**Inequalities with Addition and Subtraction

Suppose your favorite baseball team had

**Inequalities Using Addition or Subtraction**

To solve inequalities, you need the Addition Property of Inequality.

The **Addition Property of Inequality **states that 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.

#### Let's solve the following inequalities:

- Solve for
x: x−3<10 .

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?

- Solve for
x: x+4>13 .

The solution is shown below in a graph:

- Solve for
x :x+23≥−13 .

### Examples

#### Example 1

Earlier, you were told that your favorite baseball team had

This year, if the team wins 10 more games than it did last year, it will win

To solve this, subtract 10 from both sides of the inequality:

#### Example 2

Solve for

### Review

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 .

### Review (Answers)

To see the Review answers, open this PDF file and look for section 6.2.

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### Image Attributions

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

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