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x=-\frac{1}{2}+\frac{2}{3}
Add \frac{2}{3} to both sides.
x=-\frac{3}{6}+\frac{4}{6}
Least common multiple of 2 and 3 is 6. Convert -\frac{1}{2} and \frac{2}{3} to fractions with denominator 6.
x=\frac{-3+4}{6}
Since -\frac{3}{6} and \frac{4}{6} have the same denominator, add them by adding their numerators.
x=\frac{1}{6}
Add -3 and 4 to get 1.