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Chapter 2: Q. 2.145 (page 204)

Graph the solution and write the solution in interval notation:|x|<9

Short Answer

Expert verified

The solution of the inequality is-9,9.

The graph of the solution is shown below:

Step by step solution

01

Step 1. Given Information.

We have:

x<9

02

Step 2. Write the equivalent inequality and draw into the number line.  

x<9

Apply absolute rule: If鈥�|u|鈥�<鈥�a,鈥�a>0鈥�then鈥�-a鈥�<鈥�u鈥�<鈥�a

-9<x<9

03

Step 3. Draw the solution on the number line.

Draw solution -9<x<9on the number line:

Interval notation:-9,9

04

Step 4. Check each solution. 

To verify, check a value in each section of the number line showing the solution. Choose numbers such as -10,1,and 10.

|x|<9

|-10|<910<9

False.

|x|<91<9

True.

|x|<9|10|<9

True.

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