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How many solutions are there to the equation
|x| = -1/2 x + 4?

 Apr 9, 2022
 #1
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There is only one solution, x = -8.

 Apr 9, 2022
 #2
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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.

 Apr 9, 2022

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