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-\frac{1}{2}x<-3
Subtract 3 from both sides. Anything subtracted from zero gives its negation.
x>-3\left(-2\right)
Multiply both sides by -2, the reciprocal of -\frac{1}{2}. Since -\frac{1}{2} is negative, the inequality direction is changed.
x>6
Multiply -3 and -2 to get 6.