Question

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

Answer 1

`y = x - 5 " " 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 " " 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