Answer:
A) x = 3/2 or x= 1/4
Step-by-step explanation:
Solve for x
|3x − 2| = |x + 1|
Rewrite the absolute value equation as four equations without absolute value bars.
3x − 2 = x + 1
3x − 2 = − (x + 1)
− (3x − 2) = x + 1
− (3x − 2) = − (x + 1)
After simplifying, there are only two unique equations to be solved.
3x − 2 = x + 1
3x − 2 = − (x + 1)
Solve 3x − 2 = x + 1 for x.
Move all terms containing x to the left side of the equation.
2x − 2 = 1
Move all terms not containing x to the right side of the equation.
2x = 3
Divide each term by 2 and simplify.
3
x = ------
2
Solve 3x − 2 = − (x + 1) for x.
Simplify − (x + 1).
3x − 2 = −x − 1
Move all terms containing x to the left side of the equation.
4x − 2 = −1
Move all terms not containing x to the right side of the equation.
4x = 1
Divide each term by 4 and simplify.
1
x = ------
4
