Question

How do you solve 9| x+8 | + 10 < 55 & how is it graphed

Answer 1

Hello!

First, let's write the problem.
$9\left|x+8\right|+10\ \textless \ 55|x+8|+10\ \textless \ 55$
Subtract 10 from both sides.
$9\left|x+8\right|+10-10\ \textless \ 55-10$
$9\left|x+8\right|\ \textless \ 45$
Divide both sides by 9.
$\frac{9\left|x+8\right|}{9}\ \textless \ \frac{45}{9}$
$\left|x+8\right|\ \textless \ 5$
When we got absolute value, we are going to get two results.
$x+8\ \textless \ 5$
and
$x+8\ \textgreater \ -5$

Let's solve the first one,
$x+8\ \textless \ 5x+8\ \textless \ 5$
Subtract 8 from both sides.
$x+8-8\ \textless \ 5-8$
$x\ \textless \ -3x\ \textless \ -3$

Let's solve the second one.
$x+8\ \textgreater \ -5$
Subtract 8 from both sides.
$x+8-8\ \textgreater \ -5-8$
$x\ \textgreater \ -13x\ \textgreater \ -13$

Let's combine the ranges.
$-13\ \textless \ x\ \textless \ -3$

The attachment shows how would you graph it.
You can feel free to let me know if you have any questions regarding this.
Thanks!

- TetraFish