How many solutions are there to the equation |x| = -1/2 x + 4?
There is only one solution, x = -8.
If x is positive:
\(x=-\frac{1}{2}x+4\)
\(\frac{3}{2}x = 4\)
\(x = \boxed{\frac{8}{3}}\)
If x is negative:
\(-x = -\frac{1}{2}x+4\)
\(x = \frac{1}{2}x-4\)
\(\frac{1}{2}x=-4\)
\(x = \boxed{-8}\)
There are two solutions: x = 8/3, -8.
