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

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Answer 1 · 2016-07-22T16:01:59

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

The definition of $|a|$ is:
$a$ if $a>=0$
$-a$ if $a<=0$

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

So, let break down the problem into two parts:

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

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

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

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