Question

1.)Solve the absolute value equation.

2|3x -5| -8 =8

A. X= -1 5/6 or X= 5/6
B. X= -1 or X= 4 1/3
C. X= -1 5/6 or X= 4 1/3
D. X= -1 5/6 or X= -1


2.)Solve the equation. Check for extraneous solutions.
6|6 - 4x| = 8x +4

A. X=1
B. X=5/2 or X=2
C. X=5/2
D. X=5/2 or X=1

3.)Solve the inequality.
8 | X + 3/4 | <2

A. X<-1 or X>-1/2
B. -5/32 C. -1 D. X<-5/32 or X>5/32

Thank you so much for any help I'm really stuck on these three!

Answer 1

2|3x - 5| - 8 = 8
2|3x - 5| = 8 + 8 = 16
|3x - 5| = 16/2 = 8
3x - 5 = 8 or 3x - 5 = -8
3x = 8 + 5 = 13 or 3x = -8 + 5 = -3
x = 13/3 = 4 1/3 or x = -3/3 = -1

6|6 - 4x| = 8x +4
|6 - 4x| = 8/6 x + 4/6 = 4/3 x + 2/3
6 - 4x = 4/3 x + 2/3 or 6 - 4x = -4/3 x - 2/3
4/3 x + 4x = 6 - 2/3 or -4/3 x + 4x = 6 + 2/3
16/3 x = 16/3 or 8/3 x = 20/3
x = 1 or x = 5/2

8|x + 3/4| < 2
|x + 3/4| < 2/8
x + 3/4 < 1/4 or x + 3/4 > -1/4
x < 1/4 - 3/4 or x > -1/4 - 3/4
x < -1/2 or x > -1
-1 < x < -1/2