# How do you solve - 5| x + 1| = -10 ?

May 29, 2016

See below.

#### Explanation:

Firstly we can simplify this to:
$| x + 1 | = 2$

Then there's two ways of doing it:

Case analysis (the generally most preferred method for simple ones like this):

Consider if $x + 1$ is positive:
Then: $x + 1 = 2$ so $x = 1$
Consider if $x + 1$ is negative:
Then: $- \left(x + 1\right) = 2$ so $x = - 3$
(We take the negative of the left side since we want it to be positive and we've assumed it to already be negative, and two negatives make a positive, which is necessary for the absolute symbols since they always give a positive value by definition).

An alternative method, my personal favourite since it's more rigid:
$| x + 1 | = 2$
We can square both sides, since the left side will definitely be positive after it has been squared (by definition of real numbers):
${\left(x + 1\right)}^{2} = 4$
${x}^{2} + 2 x + 1 = 4$
${x}^{2} + 2 x - 3 = 0$
$\left(x + 3\right) \left(x - 1\right) = 0$
$x = 1 \mathmr{and} - 3$