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\frac{1}{2}x+3=0
Swap sides so that all variable terms are on the left hand side.
\frac{1}{2}x=-3
Subtract 3 from both sides. Anything subtracted from zero gives its negation.
x=-3\times 2
Multiply both sides by 2, the reciprocal of \frac{1}{2}.
x=-6
Multiply -3 and 2 to get -6.