How do I solve the following absolute value equation?

Question

I'm having trouble solving this equation:

$$|x+1| = |2x-2|$$

For $x+1 = 2x-2$ and $-(x+1) = -(2x-2)$ I received $x = 3$

and for $-(x+1) = 2x-2$ and $x+1 = -(2x-2)$ I received $x = 1/3$

I tried plugging both into the original equation but they don't always equal.

Answer 1

Both solutions work out, for 3: $$ | 3 + 1 | = |2(3) - 2 | $$ $$ | 4 | = | 6 - 2 | $$ $$ 4 = 4 $$

For 1/3:

$$|1/3+1| = |2(1/3) - 2 | $$ $$ 4/3 = | 2/3 - 2 | $$ $$4/3 = | 2/3 - 6/3 | $$ $$4/3 = 4/3$$