2=|-3 + 3x|?

Question

Case 1 case 2 its bugging me that this simple of an equation is becoming so difficult for me.

Answer 1

There are 2 solutions
1)
2=-3+3x add 3 to each side
5=3x divide both sides by 3
x=5/3

2)
2=-(-3+3x)
2=3-3x subtract 3 from each side
-1=-3x divide both sides by -3
x=1/3

x=1/3, 5/3

Answer 2

In dealing with absolute values (ABS), there are two possible solutions, the (-3 + 3x) will either equal 2 or -2 (since the ABS of 2 is 2 and the ABS of -2 is also 2).

Case 1:
-3 + 3x = 2 -----> 3x = 5 -----> x = 5/3

Case 2:
-3 + 3x = -2 -----> 3x = 1 -----> x = 1/3

Answer 3

This has two cases, one when the expression inside the absolute value signs is positive and one when it is negative.

Case 1: Positive
2 = +(-3 + 3x) = 3x - 3
5 = 3x
x = 5/3

Case 2: Negative
2 = -(-3 + 3x) = -3x + 3
3x = 1
x = 1/3

So the answer is
x = 1/3, 5/3

Answer 4

You have two possibilities when you've got absolute value issues. One is positive:
2 = +(3 + 3x)
2 = 3 + 3x
-1 = 3x
x = -1/3

The other is negative:
2 = -(3 + 3x)
2 = -3 - 3x
3x = -3 -2 = -5
x = -5/3

So your two possible answers are -1/3 and -5/3