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-x=\frac{1}{2}-\frac{5}{6}
Subtract \frac{5}{6} from both sides.
-x=\frac{3}{6}-\frac{5}{6}
Least common multiple of 2 and 6 is 6. Convert \frac{1}{2} and \frac{5}{6} to fractions with denominator 6.
-x=\frac{3-5}{6}
Since \frac{3}{6} and \frac{5}{6} have the same denominator, subtract them by subtracting their numerators.
-x=\frac{-2}{6}
Subtract 5 from 3 to get -2.
-x=-\frac{1}{3}
Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.
x=\frac{1}{3}
Multiply both sides by -1.