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Chapter 2: Q. 2.149 (page 205)

Solve|x|>2. Graph the solution and write the solution in interval notation.

Short Answer

Expert verified

The solution of the inequality is x<-2,x>2.

Interval notation: -鈭�鈥�,鈥�-2鈭�2,鈥�鈭�鈥�

The graph on the number line is:

Step by step solution

01

Step 1. Write the equivalent inequality. 

We have:

x>2

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

x<-2or鈥�x>2

02

Step 2. Graph the solution. 

Plot the point -2on the number line with an open circle since it is not included in the inequality. Plot the point 2on the number line with open circle since it is not included in the inequality.

Draw on the number line:

03

Step 3. Check the solution.

To verify, check the value in each section of the number line showing the solution. Choose the number such as -4,0,and7.

x>鈥�2-4>鈥�24>2

True.

x>鈥�20>鈥�20>2

False.

x>鈥�27>鈥�27>2

True.

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