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

Question

1407 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