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Chapter 2: Q. 425 (page 196)

Solve the inequality, graph the solution on the number line, and write the solution in interval notation:

-5鈮�3x-2鈮�4

Short Answer

Expert verified

The solution of the inequality:-1鈮�x鈮�2

Interval notation:-1,2

The graph of the inequality on number line is:

Step by step solution

01

Step 1. Given Information. 

We have:

-5鈮�3x-2鈮�4

02

Step 2. Solve the inequality. 

The inequality -5鈮�3x-2鈮�4can be written as-5鈮�3x-2and3x-2鈮�4

by using the property of inequality.

First, solve -5鈮�3x-2:

Switch sides:

3x-2鈮�鈥�-53x-2+2鈮�鈥�-5+23x鈮�鈥�-33x3鈮�-33x鈮�鈥�-1

Now, solve 3x-2鈮�4:

Add 2to both sides:

3x-2+2鈮�鈥�4+23x鈮�鈥�63x3鈮�63x鈮�鈥�2

03

Step 3. Draw the solution on the number line.   

We have the solution x鈮�鈥�-1and x鈮�鈥�2.

By combining the both solutions, we get -1鈮�x鈮�2.

Draw the solution on the number line:

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