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\frac{1}{2}x+\frac{1}{2}-\frac{\frac{4}{3}}{\frac{1}{6}}=2
Use the distributive property to multiply \frac{1}{2} by x+1.
\frac{1}{2}x+\frac{1}{2}-\frac{4}{3}\times 6=2
Divide \frac{4}{3} by \frac{1}{6} by multiplying \frac{4}{3} by the reciprocal of \frac{1}{6}.
\frac{1}{2}x+\frac{1}{2}-\frac{4\times 6}{3}=2
Express \frac{4}{3}\times 6 as a single fraction.
\frac{1}{2}x+\frac{1}{2}-\frac{24}{3}=2
Multiply 4 and 6 to get 24.
\frac{1}{2}x+\frac{1}{2}-8=2
Divide 24 by 3 to get 8.
\frac{1}{2}x+\frac{1}{2}-\frac{16}{2}=2
Convert 8 to fraction \frac{16}{2}.
\frac{1}{2}x+\frac{1-16}{2}=2
Since \frac{1}{2} and \frac{16}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{1}{2}x-\frac{15}{2}=2
Subtract 16 from 1 to get -15.
\frac{1}{2}x=2+\frac{15}{2}
Add \frac{15}{2} to both sides.
\frac{1}{2}x=\frac{4}{2}+\frac{15}{2}
Convert 2 to fraction \frac{4}{2}.
\frac{1}{2}x=\frac{4+15}{2}
Since \frac{4}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.
\frac{1}{2}x=\frac{19}{2}
Add 4 and 15 to get 19.
x=\frac{19}{2}\times 2
Multiply both sides by 2, the reciprocal of \frac{1}{2}.
x=19
Cancel out 2 and 2.