# How do you solve #abs(2x-3) - abs(x+4) = 8#?

##### 1 Answer

There are 2 values of

and

So we need to consider 3 ranges:

and

**If #x<-4# **

the arguments of both absolute values are negative, so without absolute values the equations could be re-written as

which would imply

**but**

** If

then only the

which implies

If

then neither absolute value function has any effect and the equation could equivalently be written as

which implies

The only two valid solutions are

and

graph{abs(2x-3)-abs(x+4)-8 [-28.86, 28.85, -14.43, 14.43]}