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-\frac{227x}{54}+\frac{431}{120}
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-\frac{227x}{54}+\frac{431}{120}
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\frac{4}{5}+\frac{7}{9}\left(6-\frac{22}{3}x\right)-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Combine -9x and \frac{5}{3}x to get -\frac{22}{3}x.
\frac{4}{5}+\frac{7}{9}\times 6+\frac{7}{9}\left(-\frac{22}{3}\right)x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Use the distributive property to multiply \frac{7}{9} by 6-\frac{22}{3}x.
\frac{4}{5}+\frac{7\times 6}{9}+\frac{7}{9}\left(-\frac{22}{3}\right)x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Express \frac{7}{9}\times 6 as a single fraction.
\frac{4}{5}+\frac{42}{9}+\frac{7}{9}\left(-\frac{22}{3}\right)x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Multiply 7 and 6 to get 42.
\frac{4}{5}+\frac{14}{3}+\frac{7}{9}\left(-\frac{22}{3}\right)x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Reduce the fraction \frac{42}{9} to lowest terms by extracting and canceling out 3.
\frac{4}{5}+\frac{14}{3}+\frac{7\left(-22\right)}{9\times 3}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Multiply \frac{7}{9} times -\frac{22}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{4}{5}+\frac{14}{3}+\frac{-154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Do the multiplications in the fraction \frac{7\left(-22\right)}{9\times 3}.
\frac{4}{5}+\frac{14}{3}-\frac{154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Fraction \frac{-154}{27} can be rewritten as -\frac{154}{27} by extracting the negative sign.
\frac{12}{15}+\frac{70}{15}-\frac{154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{14}{3} to fractions with denominator 15.
\frac{12+70}{15}-\frac{154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Since \frac{12}{15} and \frac{70}{15} have the same denominator, add them by adding their numerators.
\frac{82}{15}-\frac{154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Add 12 and 70 to get 82.
\frac{82}{15}-\frac{154}{27}x-\frac{3}{4}\times \frac{5}{2}-\frac{3}{4}\left(-2\right)x
Use the distributive property to multiply -\frac{3}{4} by \frac{5}{2}-2x.
\frac{82}{15}-\frac{154}{27}x+\frac{-3\times 5}{4\times 2}-\frac{3}{4}\left(-2\right)x
Multiply -\frac{3}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{82}{15}-\frac{154}{27}x+\frac{-15}{8}-\frac{3}{4}\left(-2\right)x
Do the multiplications in the fraction \frac{-3\times 5}{4\times 2}.
\frac{82}{15}-\frac{154}{27}x-\frac{15}{8}-\frac{3}{4}\left(-2\right)x
Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.
\frac{82}{15}-\frac{154}{27}x-\frac{15}{8}+\frac{-3\left(-2\right)}{4}x
Express -\frac{3}{4}\left(-2\right) as a single fraction.
\frac{82}{15}-\frac{154}{27}x-\frac{15}{8}+\frac{6}{4}x
Multiply -3 and -2 to get 6.
\frac{82}{15}-\frac{154}{27}x-\frac{15}{8}+\frac{3}{2}x
Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.
\frac{656}{120}-\frac{154}{27}x-\frac{225}{120}+\frac{3}{2}x
Least common multiple of 15 and 8 is 120. Convert \frac{82}{15} and \frac{15}{8} to fractions with denominator 120.
\frac{656-225}{120}-\frac{154}{27}x+\frac{3}{2}x
Since \frac{656}{120} and \frac{225}{120} have the same denominator, subtract them by subtracting their numerators.
\frac{431}{120}-\frac{154}{27}x+\frac{3}{2}x
Subtract 225 from 656 to get 431.
\frac{431}{120}-\frac{227}{54}x
Combine -\frac{154}{27}x and \frac{3}{2}x to get -\frac{227}{54}x.
\frac{4}{5}+\frac{7}{9}\left(6-\frac{22}{3}x\right)-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Combine -9x and \frac{5}{3}x to get -\frac{22}{3}x.
\frac{4}{5}+\frac{7}{9}\times 6+\frac{7}{9}\left(-\frac{22}{3}\right)x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Use the distributive property to multiply \frac{7}{9} by 6-\frac{22}{3}x.
\frac{4}{5}+\frac{7\times 6}{9}+\frac{7}{9}\left(-\frac{22}{3}\right)x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Express \frac{7}{9}\times 6 as a single fraction.
\frac{4}{5}+\frac{42}{9}+\frac{7}{9}\left(-\frac{22}{3}\right)x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Multiply 7 and 6 to get 42.
\frac{4}{5}+\frac{14}{3}+\frac{7}{9}\left(-\frac{22}{3}\right)x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Reduce the fraction \frac{42}{9} to lowest terms by extracting and canceling out 3.
\frac{4}{5}+\frac{14}{3}+\frac{7\left(-22\right)}{9\times 3}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Multiply \frac{7}{9} times -\frac{22}{3} by multiplying numerator times numerator and denominator times denominator.
\frac{4}{5}+\frac{14}{3}+\frac{-154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Do the multiplications in the fraction \frac{7\left(-22\right)}{9\times 3}.
\frac{4}{5}+\frac{14}{3}-\frac{154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Fraction \frac{-154}{27} can be rewritten as -\frac{154}{27} by extracting the negative sign.
\frac{12}{15}+\frac{70}{15}-\frac{154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Least common multiple of 5 and 3 is 15. Convert \frac{4}{5} and \frac{14}{3} to fractions with denominator 15.
\frac{12+70}{15}-\frac{154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Since \frac{12}{15} and \frac{70}{15} have the same denominator, add them by adding their numerators.
\frac{82}{15}-\frac{154}{27}x-\frac{3}{4}\left(\frac{5}{2}-2x\right)
Add 12 and 70 to get 82.
\frac{82}{15}-\frac{154}{27}x-\frac{3}{4}\times \frac{5}{2}-\frac{3}{4}\left(-2\right)x
Use the distributive property to multiply -\frac{3}{4} by \frac{5}{2}-2x.
\frac{82}{15}-\frac{154}{27}x+\frac{-3\times 5}{4\times 2}-\frac{3}{4}\left(-2\right)x
Multiply -\frac{3}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{82}{15}-\frac{154}{27}x+\frac{-15}{8}-\frac{3}{4}\left(-2\right)x
Do the multiplications in the fraction \frac{-3\times 5}{4\times 2}.
\frac{82}{15}-\frac{154}{27}x-\frac{15}{8}-\frac{3}{4}\left(-2\right)x
Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.
\frac{82}{15}-\frac{154}{27}x-\frac{15}{8}+\frac{-3\left(-2\right)}{4}x
Express -\frac{3}{4}\left(-2\right) as a single fraction.
\frac{82}{15}-\frac{154}{27}x-\frac{15}{8}+\frac{6}{4}x
Multiply -3 and -2 to get 6.
\frac{82}{15}-\frac{154}{27}x-\frac{15}{8}+\frac{3}{2}x
Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.
\frac{656}{120}-\frac{154}{27}x-\frac{225}{120}+\frac{3}{2}x
Least common multiple of 15 and 8 is 120. Convert \frac{82}{15} and \frac{15}{8} to fractions with denominator 120.
\frac{656-225}{120}-\frac{154}{27}x+\frac{3}{2}x
Since \frac{656}{120} and \frac{225}{120} have the same denominator, subtract them by subtracting their numerators.
\frac{431}{120}-\frac{154}{27}x+\frac{3}{2}x
Subtract 225 from 656 to get 431.
\frac{431}{120}-\frac{227}{54}x
Combine -\frac{154}{27}x and \frac{3}{2}x to get -\frac{227}{54}x.
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Limits
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