What is the solution set for absx < 15?

Aug 14, 2015

$- 15 < x < 15$

Explanation:

All you really have to do to solve this absolute value inequality is to take into account the two possible signs $x$ can have.

• $x > 0 \implies | x | = x$

In this case, the inequality becomes

$x < 15$

• $x < 0 \implies | x | = - x$

This time, you have

$- x < 15 \implies x > - 15$

So, the solution set to this inequality will include any value of $x$ that simultaneously satisfies these conditions, $x > - 15$ and $x < 15$.

Therefore, the solution set will be $- 15 < x < 15$, or $x \in \left(- 15 , 15\right)$.