Answer:
-5 < x < 31
Step-by-step 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
