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\frac{2}{3}x+\frac{2}{3}\left(-5\right)-\frac{1}{4}\left(x-2\right)=\frac{9}{2}
Use the distributive property to multiply \frac{2}{3} by x-5.
\frac{2}{3}x+\frac{2\left(-5\right)}{3}-\frac{1}{4}\left(x-2\right)=\frac{9}{2}
Express \frac{2}{3}\left(-5\right) as a single fraction.
\frac{2}{3}x+\frac{-10}{3}-\frac{1}{4}\left(x-2\right)=\frac{9}{2}
Multiply 2 and -5 to get -10.
\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}\left(x-2\right)=\frac{9}{2}
Fraction \frac{-10}{3} can be rewritten as -\frac{10}{3} by extracting the negative sign.
\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x-\frac{1}{4}\left(-2\right)=\frac{9}{2}
Use the distributive property to multiply -\frac{1}{4} by x-2.
\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{-\left(-2\right)}{4}=\frac{9}{2}
Express -\frac{1}{4}\left(-2\right) as a single fraction.
\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{2}{4}=\frac{9}{2}
Multiply -1 and -2 to get 2.
\frac{2}{3}x-\frac{10}{3}-\frac{1}{4}x+\frac{1}{2}=\frac{9}{2}
Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.
\frac{5}{12}x-\frac{10}{3}+\frac{1}{2}=\frac{9}{2}
Combine \frac{2}{3}x and -\frac{1}{4}x to get \frac{5}{12}x.
\frac{5}{12}x-\frac{20}{6}+\frac{3}{6}=\frac{9}{2}
Least common multiple of 3 and 2 is 6. Convert -\frac{10}{3} and \frac{1}{2} to fractions with denominator 6.
\frac{5}{12}x+\frac{-20+3}{6}=\frac{9}{2}
Since -\frac{20}{6} and \frac{3}{6} have the same denominator, add them by adding their numerators.
\frac{5}{12}x-\frac{17}{6}=\frac{9}{2}
Add -20 and 3 to get -17.
\frac{5}{12}x=\frac{9}{2}+\frac{17}{6}
Add \frac{17}{6} to both sides.
\frac{5}{12}x=\frac{27}{6}+\frac{17}{6}
Least common multiple of 2 and 6 is 6. Convert \frac{9}{2} and \frac{17}{6} to fractions with denominator 6.
\frac{5}{12}x=\frac{27+17}{6}
Since \frac{27}{6} and \frac{17}{6} have the same denominator, add them by adding their numerators.
\frac{5}{12}x=\frac{44}{6}
Add 27 and 17 to get 44.
\frac{5}{12}x=\frac{22}{3}
Reduce the fraction \frac{44}{6} to lowest terms by extracting and canceling out 2.
x=\frac{22}{3}\times \frac{12}{5}
Multiply both sides by \frac{12}{5}, the reciprocal of \frac{5}{12}.
x=\frac{22\times 12}{3\times 5}
Multiply \frac{22}{3} times \frac{12}{5} by multiplying numerator times numerator and denominator times denominator.
x=\frac{264}{15}
Do the multiplications in the fraction \frac{22\times 12}{3\times 5}.
x=\frac{88}{5}
Reduce the fraction \frac{264}{15} to lowest terms by extracting and canceling out 3.