Two Answers: x = 2 or x = -10
=====================================================
Work Shown:
|3x+12| = 18
3x+12 = 18 or 3x+12 = -18
3x = 18-12 or 3x = -18-12
3x = 6 or 3x = -30
x = 6/3 or x = -30/3
x = 2 or x = -10
The rule used in step 2 is the idea that if |x| = k, for some positive number k, then x = k or x = -k. One equation breaks into two separate ones. From there we solve each equation for x as normal. Follow PEMDAS in reverse, undoing each operation, to isolate x.
If you're curious why the absolute value breaks into two parts, consider something like |x| = 7. This means x is 7 units away from zero on a number line. There are two possible locations where x could be: 7 and -7. This is one example showing why we get two different results. The same applies to our equation as well, just it's a bit more complicated.