# How do you solve 3(abs(x-1)+2)=30?

May 10, 2015

The solutions are $x = - 7$ and $x = 9$.

Starting with $3 \left(| x - 1 | + 2\right) = 30$, first divide both sides by 3 to give:
$| x - 1 | + 2 = 10$.

Subtract 2 from both sides to give:
$| x - 1 | = 8$

Hence
$x - 1 = \pm 8$

Add 1 to both sides to get:
$x = \pm 8 + 1$

So $x = - 8 + 1 = - 7$ or $x = 8 + 1 = 9$.