Question

Which of the following is (are) the solution(s) to |x-13|<18

Answer 1

The full answer in the media.Good luck!

Answer 2

-5 < x < 31

Explanation:

Step 1 :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy 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

Solution in Interval Notation

(-5,31)

Solution on the Number Line

One solution was found :

-5 < x < 31