# How do you solve the inequality x+5<abs(x+5) and write your answer in interval notation?

Feb 20, 2017

$\left(- \infty , - 5\right)$

#### Explanation:

For $x > = - 5$, we have $\left\mid x + 5 \right\mid = x + 5$ so there are no solutions greater than or equal to $- 5$.

For $x < - 5$, we have $x + 5 < 0 \le \left\mid x + 5 \right\mid$

So the solution set is $\left(- \infty , - 5\right)$

Another explanation

If $a$ is positive, then $a = \left\mid a \right\mid$

Is $a$ is negative, then $a < \left\mid a \right\mid$

$x + 5$ is negative for $x < - 5$