How do you solve and write the following in interval notation:  | 5x + 3 | >18?

Jun 24, 2016

When you have the absolute value, you can remove it considering the two sign $\setminus \pm$. You have to be careful with the inequality because the $+$ keep the direction of the inequality while the $-$ inverte it.
$| 5 x + 3 | > 18$
$5 x + 3 > 18$ and $5 x + 3 < - 18$
$5 x > 15$ and $5 x < - 21$
$x > 3$ and $x < - \frac{21}{5}$.
As interval you can say that $x \in \left(- \infty , - \frac{21}{5}\right) \mathmr{and} \left(3 , + \infty\right)$.