Question 7770
Alright. The 4 is not being multiplied by the absolute value, so move it to the right by subtracting it. So far, you should get:


{{{ -3abs(x-2) = -12 }}} <--- combined the -4 and the -8.


{{{ abs(x-2) = 4 }}} <---- divide both sides by -3.


Now here's the tricky part. Just by looking at it, it's so tempting to say that x = 6 because 6 - 4 = 2. And that's right. BUT, there is ANOTHER solution!


Actually, when you solve absolute value equations, you actually solve 2 equations. In this case, the two are {{{ x - 2 = 4 }}} which was what we did, and {{{ x - 2 = -4 }}}. Why, though, do we do that!?


We know that |4| = 4, right? So we set the inside of the absolute value x - 2 to equal four. BUT we also know that |-4| = 4. AHA! So it then makes sense to set the inside of the absolute value equal to -4. After all, it'll turn that -4 into a positive 4.


SO, let's nail down the x - 2 = -4 also. It turns out (by adding 2 to both sides) that x = -2. If we plugged that into the absolute value, we have |-2 - 2| = |-4| = 4.


So your solutions are 6 and -2.