How do you solve abs(x+5)=4?

Jul 22, 2016

You have to use the definition of $| a |$

Explanation:

The definition of $| a |$ is:
$a$ if $a \ge 0$
$- a$ if $a \le 0$

For example, $| 5 | = 5$, $| - 5 | = 5$, and $| 0 | = 0$

So, let break down the problem into two parts:

$| x + 5 | \ge 0$; in this case $| x + 5 | = x + 5$, and the equation is $x + 5 = 4$, so $x = - 1$

$| x + 5 | < 0$; in this case $| x + 5 | = - \left(x + 5\right) = - x - 5$, and the equation is $- x - 5 = 4$, so $x = - 9$

The solutions are then $x = - 1$ and $x = - 9$