# How do you solve  abs(x+5)>12?

Aug 31, 2015

$x \in \left(- \infty , - 17\right) \cup \left(7 , + \infty\right)$

#### Explanation:

You're dealing with the absolute value of an expression, which means that you need totake into account the fact that the absolute value of a real number returns a positive value regardless of the sign of said number.

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This means that you have to look at two possible scenarios, one in which the expression inside the modulus is positive and one in which it's negative.

• $x + 5 > 0 \implies | x + 5 | = x + 5$

The inequality takes the form

$x + 5 > 12 \implies x > 7$

• $x + 5 < 0 \implies | x + 5 | = - \left(x + 5\right)$

This time, you get

$- \left(x + 5\right) > 12$

$- x - 5 > 12$

$- x > 17 \implies x < - 17$

The inequality will be true for any value of $x$ that is greater than $7$ or smaller than $\left(- 17\right)$. The solution set will thus be $x \in \left(- \infty , - 17\right) \cup \left(7 , + \infty\right)$.