# How do you solve the inequality: abs(x - 8) < 5?

Aug 14, 2015

$3 < x < 13$

#### Explanation:

In order to solve this absolute value inequality, you need totake into account the two possible signs the expression inside the modulus can have

• $x - 8 > 0 \implies | x - 8 | = x - 8$

The inequality will become

$x - 8 < 5$

$x < 13$

• $x - 8 < 0 \implies | x - 8 | = - \left(x - 8\right)$

This time, the inequality will be

$- \left(x - 8\right) < 5$

$- x + 8 < 5$

$x > 3$

So, the solution set for this inequality will include any value of $x$ that is bigger than $3$ and smaller than $13$.

This means that you have $3 < x < 13$, or $x \in \left(3 , 13\right)$.