# How do you solve 5abs(q + 6)=20?

Apr 3, 2015

q=-2; q=-10

Given: $5 \left\mid q + 6 \right\mid = 20$
$\left\mid q + 6 \right\mid = 4$

Absolute value is the distance a given number is from zero. This means that $q + 6 = 4$ or $q + 6 = - 4$

$q + 6 = 4$
$q = - 2$

$q + 6 = - 4$
$q = - 10$

I hope that was helpful.

Apr 3, 2015

Consider two possibilities:
$q < - 6$ and $q \succ 6$
(note by observation we can eliminate $q = - 6$)

If $q < - 6$
then $\left(q + 6\right)$ is negative and
$\left\mid q + 6 \right\mid$ is equivalent to $- \left(q + 6\right)$
and the equation becomes
$5 \left(- \left(q + 6\right)\right) = 20$
$- q - 6 = 4$
$q = - 10$

If $q \succ 6$
then $\left(q + 6\right)$ is positive and
$\left\mid q + 6 \right\mid$ is equivalent to $\left(q + 6\right)$
and the equation becomes:
$5 \left(q + 6\right) = 20$
$q + 6 = 4$
$q = - 2$

The two solutions to this equation are
$q = - 10$ and $q = - 2$