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

Question

2055 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-18T22:51:41

$y = x - 5 " " or " " y = -x -5$

$x ge 0$

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

$a = |b|$

$a = b " " or " " a = -b$

In this case, we have the following two equations:

$x = |y+5|$

$x = y + 5 " " or " " x = -(y+5)$

$x - 5 = y " " or " " x + 5 = -y$

$x - 5 = y " " or " " -x-5 = y$

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.

Final Answer

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