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4+\frac{1}{2}x-x=0
Subtract x from both sides.
4-\frac{1}{2}x=0
Combine \frac{1}{2}x and -x to get -\frac{1}{2}x.
-\frac{1}{2}x=-4
Subtract 4 from both sides. Anything subtracted from zero gives its negation.
x=-4\left(-2\right)
Multiply both sides by -2, the reciprocal of -\frac{1}{2}.
x=8
Multiply -4 and -2 to get 8.