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\frac{1}{2}x\leq -3+3
Add 3 to both sides.
\frac{1}{2}x\leq 0
Add -3 and 3 to get 0.
x\leq 0
Product of two numbers is ≤0 if one is ≥0 and the other is ≤0. Since \frac{1}{2}\geq 0, x must be ≤0.