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

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Answer 1 · 2015-04-03T01:47:16

$q=-2; q=-10$

Given: $5abs(q + 6) = 20$
$abs(q+6) = 4$

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.

Answer 2 · 2015-04-03T01:50:01

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

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

If $q>-6$
then $(q+6)$ is positive and
$abs(q+6)$ is equivalent to $(q+6)$
and the equation becomes:
$5(q+6) = 20$
$q+6 = 4$
$q=-2$

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

How do you solve 5abs(q + 6)=205abs(q + 6)=20?