2 POINTS
which of the following is the solution to | x-13|<18

 -5 < x < 31

Step-by-step explanation:

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequality entered

     |x-13| < 18  

Step  2  :

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |x-13|

For the Negative case we'll use -(x-13)  

For the Positive case we'll use (x-13)  

Step  3  :

Solve the Negative Case

     -(x-13) < 18  

    Multiply

     -x+13 < 18  

    Rearrange and Add up

     -x < 5  

    Multiply both sides by (-1)

    Remember to flip the inequality sign

     x > -5  

    Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

     (x-13) < 18  

    Rearrange and Add up

     x < 31  

    Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

   -5 < x < 31

x = 23.78

step-by-step explanation: