|3x-2| = 0 — ignore absolute value for a sec, add 2

3x = 2 — divide by 3

x = 2/3

now plug that into the original equation with a plus and a minus:

8 l 3x-2 l = 0

8 | 2-2 | = 0

8 | 0| = 0 (positive 2/3 works)

8 | -2 – 2 | = 0

8 |-4| = 0

32 = 0 (negative 2/3 doesn’t work)

so your only answer is 2/3

divide both sides by 8

8/8 l 3x-2 l = 0/8

l 3x-2 l = 0

you don’t need to worry about the absolute value zero is neither a positive or negative number so 3x-2 = 0.

Add 2 to each side

3x-2+2 = 0+2

3x = 2

divide both sides by 3

3x/3 = 2/3

x = 2/3

If you go back to the original problem and plug in 2/3 for x, you will find this is the correct answer.