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