Solve for x
x\leq 2
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3-x-\frac{1}{2}x\geq 0
Subtract \frac{1}{2}x from both sides.
3-\frac{3}{2}x\geq 0
Combine -x and -\frac{1}{2}x to get -\frac{3}{2}x.
-\frac{3}{2}x\geq -3
Subtract 3 from both sides. Anything subtracted from zero gives its negation.
x\leq -3\left(-\frac{2}{3}\right)
Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}. Since -\frac{3}{2} is negative, the inequality direction is changed.
x\leq 2
Multiply -3 times -\frac{2}{3}.
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