How do you solve for y in  x = | y + 5 | ?

Oct 18, 2017

$y = x - 5 \text{ " or " } y = - x - 5$

$x \ge 0$

Explanation:

Whenever you have an absolute value problem like this, split it into two equations like so:

$a = | b |$

$a = b \text{ " or " } a = - b$

In this case, we have the following two equations:

$x = | y + 5 |$

$x = y + 5 \text{ " or " } x = - \left(y + 5\right)$

$x - 5 = y \text{ " or " } x + 5 = - y$

$x - 5 = y \text{ " or " } - x - 5 = y$

We don't know what $x$ is, though, so this is as far as we can solve.

One final thing we must note, however, is that $x$ cannot be negative, since it is equal to an absolute value term.