Answer: x=3
x=-7/3
Step-by-step explanation:
How do you find the solution to absolute value inequality?
Here are the steps to follow when solving absolute value inequalities:
Isolate the absolute value expression on the left side of the inequality.
If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions.
Step by Step Solution:
Absolute Value Equation entered :
|3x-1|=8
Step by step solution :
STEP
1
:
Rearrange this Absolute Value Equation
Absolute value equalitiy entered
|3x-1| = 8
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 |3x-1|
For the Negative case we'll use -(3x-1)
For the Positive case we'll use (3x-1)
STEP
3
:
Solve the Negative Case
-(3x-1) = 8
Multiply
-3x+1 = 8
Rearrange and Add up
-3x = 7
Divide both sides by 3
-x = (7/3)
Multiply both sides by (-1)
x = -(7/3)
Which is the solution for the Negative Case
STEP
4
:
Solve the Positive Case
(3x-1) = 8
Rearrange and Add up
3x = 9
Divide both sides by 3
x = 3
Which is the solution for the Positive Case
STEP
5
:
Wrap up the solution
x=-7/3
x=3
Solutions on the Number Line
image
Two solutions are made:
x=3
x=-7/3
