Absolute value equations have two solutions; since absolute values will always be positive, this makes sense. For example, in #abs(x) = 9#, #x# can equal 9 and -9; the absolute value of 9 equals 9 and the absolute value of -9 equals 9.

As such, we need two equations to find the two solutions. Our two equations are: #6-x = 9# and #6-x = -9#. You've probably noticed that these equations are extremely similar - except one equation equals 9, and the other -9. Always set up absolute value equations like this when you're ready to solve.

Let's get to the solving, starting with #6-x = 9#:

#6-x = 9# (original equation)

#-x = 3# (subtracting 6 from both sides)

#x = -3# (dividing by -1)

Alright, #x = -3# is one solution. Now, for #6-x = -9#:

#6-x = -9# (original equation)

#-x = -15# (subtracting 6 from both sides)

#x = 15# (dividing by -1)

And that's it. Our solutions are #x = 15# and #x = -3#.