# How do you solve 6 abs[8-y]=36?

Apr 18, 2016

You may start by dividing both sides by $6$

#### Explanation:

$\to | 8 - y | = 6$

Now there are two possiblities, depending on the value of $y$

(1) $y \le 8 \to 8 - y \ge 0$
The equation is equivalent to $8 - y = 6 \to y = 2$

(2) $y > 8 \to 8 - y < 0$
But then the aboslute bars 'flip' the sign, and the equation becomes equivalent to $- 8 + y = 6 \to y = 14$
graph{|8-x| [-6.2, 25.85, -1.89, 14.13]}

Apr 18, 2016

Algebraically, $| 8 - y | = 6$ is the combined equation for the separate equations $8 - y = 6 \mathmr{and} - \left(8 - y\right) = 6$. So, y = 2 and y = 14.