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\frac{3}{2}\left(\frac{7}{3}x+\frac{1}{3}\right)=2x+1
Multiply 3 and \frac{1}{2} to get \frac{3}{2}.
\frac{3}{2}\times \frac{7}{3}x+\frac{3}{2}\times \frac{1}{3}=2x+1
Use the distributive property to multiply \frac{3}{2} by \frac{7}{3}x+\frac{1}{3}.
\frac{3\times 7}{2\times 3}x+\frac{3}{2}\times \frac{1}{3}=2x+1
Multiply \frac{3}{2} times \frac{7}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{7}{2}x+\frac{3}{2}\times \frac{1}{3}=2x+1
Cancel out 3 in both numerator and denominator.
\frac{7}{2}x+\frac{3\times 1}{2\times 3}=2x+1
Multiply \frac{3}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{7}{2}x+\frac{1}{2}=2x+1
Cancel out 3 in both numerator and denominator.
\frac{7}{2}x+\frac{1}{2}-2x=1
Subtract 2x from both sides.
\frac{3}{2}x+\frac{1}{2}=1
Combine \frac{7}{2}x and -2x to get \frac{3}{2}x.
\frac{3}{2}x=1-\frac{1}{2}
Subtract \frac{1}{2} from both sides.
\frac{3}{2}x=\frac{2}{2}-\frac{1}{2}
Convert 1 to fraction \frac{2}{2}.
\frac{3}{2}x=\frac{2-1}{2}
Since \frac{2}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.
\frac{3}{2}x=\frac{1}{2}
Subtract 1 from 2 to get 1.
x=\frac{1}{2}\times \frac{2}{3}
Multiply both sides by \frac{2}{3}, the reciprocal of \frac{3}{2}.
x=\frac{1\times 2}{2\times 3}
Multiply \frac{1}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.
x=\frac{1}{3}
Cancel out 2 in both numerator and denominator.