Solve the absolute value equation graph solution 2|3 x-5|-8=8 answers are x=1 5/6or x=5/6, x=1 or x=4 1/3, x=1 5/6or x=4 1/3, x=1 5/6or x=-1 thank you

2|3 x-5|-8=8

2|3 x-5| = 16
|3 x-5| = 8

3x-5 = 8 or -3x+5 = 8
3x = 13 or -3x = 3
x = 13/3 OR x = -1

choose your matching answer, it is there.

To solve the equation 2|3x-5|-8=8, we need to isolate the absolute value on one side. Here's how you can solve it step by step:

Step 1: Add 8 to both sides of the equation:
2|3x-5|-8+8 = 8+8
2|3x-5| = 16

Step 2: Divide both sides of the equation by 2:
(2|3x-5|)/2 = 16/2
|3x-5| = 8

Step 3: Now, we have two cases to consider:

Case 1: (3x-5) is positive:

If (3x-5) is positive, then the equation |3x-5| = 8 becomes:
3x-5 = 8

Solving this equation gives x = 4 1/3 or x = 13/3.

Case 2: (3x-5) is negative:

If (3x-5) is negative, then the equation |3x-5| = 8 becomes:
-(3x-5) = 8

Simplifying this equation gives -3x+5 = 8.
Solving for x gives x = 1.

Therefore, the possible solutions for the equation 2|3x-5|-8=8 are:
x = 4 1/3 or x = 13/3, and
x = 1.

So the correct answer is x = 4 1/3, x = 13/3, and x = 1, which matches your answer: x = 1 or x = 4 1/3.