Solve 13/4(12/6x+2/8)+1/4(2frac{4}{8}x+frac{2}{3})+frac{3}{4}(-x-frac{1}{2})-(x-frac{1}{2})

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\frac{4+3}{4}\left(\frac{1\times 6+2}{6}x+\frac{2}{8}\right)+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Multiply 1 and 4 to get 4.

\frac{7}{4}\left(\frac{1\times 6+2}{6}x+\frac{2}{8}\right)+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Add 4 and 3 to get 7.

\frac{7}{4}\left(\frac{6+2}{6}x+\frac{2}{8}\right)+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Multiply 1 and 6 to get 6.

\frac{7}{4}\left(\frac{8}{6}x+\frac{2}{8}\right)+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Add 6 and 2 to get 8.

\frac{7}{4}\left(\frac{4}{3}x+\frac{2}{8}\right)+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Reduce the fraction \frac{8}{6} to lowest terms by extracting and canceling out 2.

\frac{7}{4}\left(\frac{4}{3}x+\frac{1}{4}\right)+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Reduce the fraction \frac{2}{8} to lowest terms by extracting and canceling out 2.

\frac{7}{4}\times \frac{4}{3}x+\frac{7}{4}\times \frac{1}{4}+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Use the distributive property to multiply \frac{7}{4} by \frac{4}{3}x+\frac{1}{4}.

\frac{7\times 4}{4\times 3}x+\frac{7}{4}\times \frac{1}{4}+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Multiply \frac{7}{4} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

\frac{7}{3}x+\frac{7}{4}\times \frac{1}{4}+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Cancel out 4 in both numerator and denominator.

\frac{7}{3}x+\frac{7\times 1}{4\times 4}+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Multiply \frac{7}{4} times \frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

\frac{7}{3}x+\frac{7}{16}+\frac{1}{4}\left(\frac{2\times 8+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Do the multiplications in the fraction \frac{7\times 1}{4\times 4}.

\frac{7}{3}x+\frac{7}{16}+\frac{1}{4}\left(\frac{16+4}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Multiply 2 and 8 to get 16.

\frac{7}{3}x+\frac{7}{16}+\frac{1}{4}\left(\frac{20}{8}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Add 16 and 4 to get 20.

\frac{7}{3}x+\frac{7}{16}+\frac{1}{4}\left(\frac{5}{2}x+\frac{2}{3}\right)+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Reduce the fraction \frac{20}{8} to lowest terms by extracting and canceling out 4.

\frac{7}{3}x+\frac{7}{16}+\frac{1}{4}\times \frac{5}{2}x+\frac{1}{4}\times \frac{2}{3}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Use the distributive property to multiply \frac{1}{4} by \frac{5}{2}x+\frac{2}{3}.

\frac{7}{3}x+\frac{7}{16}+\frac{1\times 5}{4\times 2}x+\frac{1}{4}\times \frac{2}{3}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Multiply \frac{1}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

\frac{7}{3}x+\frac{7}{16}+\frac{5}{8}x+\frac{1}{4}\times \frac{2}{3}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Do the multiplications in the fraction \frac{1\times 5}{4\times 2}.

\frac{7}{3}x+\frac{7}{16}+\frac{5}{8}x+\frac{1\times 2}{4\times 3}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Multiply \frac{1}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

\frac{7}{3}x+\frac{7}{16}+\frac{5}{8}x+\frac{2}{12}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Do the multiplications in the fraction \frac{1\times 2}{4\times 3}.

\frac{7}{3}x+\frac{7}{16}+\frac{5}{8}x+\frac{1}{6}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Reduce the fraction \frac{2}{12} to lowest terms by extracting and canceling out 2.

\frac{71}{24}x+\frac{7}{16}+\frac{1}{6}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Combine \frac{7}{3}x and \frac{5}{8}x to get \frac{71}{24}x.

\frac{71}{24}x+\frac{21}{48}+\frac{8}{48}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Least common multiple of 16 and 6 is 48. Convert \frac{7}{16} and \frac{1}{6} to fractions with denominator 48.

\frac{71}{24}x+\frac{21+8}{48}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Since \frac{21}{48} and \frac{8}{48} have the same denominator, add them by adding their numerators.

\frac{71}{24}x+\frac{29}{48}+\frac{3}{4}\left(-x-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Add 21 and 8 to get 29.

\frac{71}{24}x+\frac{29}{48}+\frac{3}{4}\left(-x\right)+\frac{3}{4}\left(-\frac{1}{2}\right)-\left(x-\frac{1}{2}\right)

Use the distributive property to multiply \frac{3}{4} by -x-\frac{1}{2}.

\frac{71}{24}x+\frac{29}{48}+\frac{3}{4}\left(-x\right)+\frac{3\left(-1\right)}{4\times 2}-\left(x-\frac{1}{2}\right)

Multiply \frac{3}{4} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

\frac{71}{24}x+\frac{29}{48}+\frac{3}{4}\left(-x\right)+\frac{-3}{8}-\left(x-\frac{1}{2}\right)

Do the multiplications in the fraction \frac{3\left(-1\right)}{4\times 2}.

\frac{71}{24}x+\frac{29}{48}+\frac{3}{4}\left(-x\right)-\frac{3}{8}-\left(x-\frac{1}{2}\right)

Fraction \frac{-3}{8} can be rewritten as -\frac{3}{8} by extracting the negative sign.

\frac{71}{24}x+\frac{29}{48}+\frac{3}{4}\left(-x\right)-\frac{18}{48}-\left(x-\frac{1}{2}\right)

Least common multiple of 48 and 8 is 48. Convert \frac{29}{48} and \frac{3}{8} to fractions with denominator 48.

\frac{71}{24}x+\frac{29-18}{48}+\frac{3}{4}\left(-x\right)-\left(x-\frac{1}{2}\right)

Since \frac{29}{48} and \frac{18}{48} have the same denominator, subtract them by subtracting their numerators.

\frac{71}{24}x+\frac{11}{48}+\frac{3}{4}\left(-x\right)-\left(x-\frac{1}{2}\right)

Subtract 18 from 29 to get 11.

\frac{71}{24}x+\frac{11}{48}+\frac{3}{4}\left(-x\right)-x-\left(-\frac{1}{2}\right)

To find the opposite of x-\frac{1}{2}, find the opposite of each term.

\frac{71}{24}x+\frac{11}{48}+\frac{3}{4}\left(-x\right)-x+\frac{1}{2}

The opposite of -\frac{1}{2} is \frac{1}{2}.

\frac{47}{24}x+\frac{11}{48}+\frac{3}{4}\left(-x\right)+\frac{1}{2}

Combine \frac{71}{24}x and -x to get \frac{47}{24}x.

\frac{47}{24}x+\frac{11}{48}+\frac{3}{4}\left(-x\right)+\frac{24}{48}

Least common multiple of 48 and 2 is 48. Convert \frac{11}{48} and \frac{1}{2} to fractions with denominator 48.

\frac{47}{24}x+\frac{11+24}{48}+\frac{3}{4}\left(-x\right)

Since \frac{11}{48} and \frac{24}{48} have the same denominator, add them by adding their numerators.

\frac{47}{24}x+\frac{35}{48}+\frac{3}{4}\left(-x\right)

Add 11 and 24 to get 35.

\frac{47}{24}x+\frac{35}{48}-\frac{3}{4}x

Multiply \frac{3}{4} and -1 to get -\frac{3}{4}.

\frac{29}{24}x+\frac{35}{48}

Combine \frac{47}{24}x and -\frac{3}{4}x to get \frac{29}{24}x.