# How do you solve the absolute value inequality and express the solution set in interval notation for -2abs(s-3)<-4?

Apr 10, 2015

Multiplying both sides of an inequality by a negative value reverses the inequality
So
$- 2 \left\mid s - 3 \right\mid < - 4$
is equivalent to
$\left\mid s - 3 \right\mid > 2$

If $\left(s - 3\right)$ is negative (i.e. $s < 3$)
then this becomes
$3 - s > 2$
$- s \succ 1$
$s < 1$

If $\left(s - 3\right)$ is positive or zero (i.e. $s \ge 3$)
then
$\left(s - 3\right) > 2$
$s > 5$

So
$s \epsilon \left(- \infty , 1\right) \bigcup \left(5 , + \infty\right)$