Question 15 (5 points) Solve |3x - 2| = |x + 1|
A) x = 3/2 or x= 1/4
B) x= 1/4
C) No solutions
D) x = 3 or x = -4

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

21

step-by-step explanation:

a) 7x=7

step-by-step explanation: