Solve -4/5+7/9(6-9x+5/3z)-3/4*(frac{5}{2}-2z)

$$- \frac { 4 } { 5 } + \frac { 7 } { 9 } ( 6 - 9 x + \frac { 5 } { 3 } z ) - \frac { 3 } { 4 } \times ( \frac { 5 } { 2 } - 2 z )$$

Evaluate

$$\frac{151z}{54}-7x+\frac{239}{120}$$

Solution Steps

Use the distributive property to multiply \frac{7}{9} by 6-9x+\frac{5}{3}z.

$$-\frac{4}{5}+\frac{7}{9}\times 6+\frac{7}{9}\left(-9\right)x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Express \frac{7}{9}\times 6 as a single fraction.

$$-\frac{4}{5}+\frac{7\times 6}{9}+\frac{7}{9}\left(-9\right)x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Multiply 7 and 6 to get 42.

$$-\frac{4}{5}+\frac{42}{9}+\frac{7}{9}\left(-9\right)x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Reduce the fraction \frac{42}{9} to lowest terms by extracting and canceling out 3.

$$-\frac{4}{5}+\frac{14}{3}+\frac{7}{9}\left(-9\right)x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Express \frac{7}{9}\left(-9\right) as a single fraction.

$$-\frac{4}{5}+\frac{14}{3}+\frac{7\left(-9\right)}{9}x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Multiply 7 and -9 to get -63.

$$-\frac{4}{5}+\frac{14}{3}+\frac{-63}{9}x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Divide -63 by 9 to get -7.

$$-\frac{4}{5}+\frac{14}{3}-7x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Multiply \frac{7}{9} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{4}{5}+\frac{14}{3}-7x+\frac{7\times 5}{9\times 3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Do the multiplications in the fraction \frac{7\times 5}{9\times 3}.

$$-\frac{4}{5}+\frac{14}{3}-7x+\frac{35}{27}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Least common multiple of 5 and 3 is 15. Convert -\frac{4}{5} and \frac{14}{3} to fractions with denominator 15.

$$-\frac{12}{15}+\frac{70}{15}-7x+\frac{35}{27}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Since -\frac{12}{15} and \frac{70}{15} have the same denominator, add them by adding their numerators.

$$\frac{-12+70}{15}-7x+\frac{35}{27}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Add -12 and 70 to get 58.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Use the distributive property to multiply -\frac{3}{4} by \frac{5}{2}-2z.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{3}{4}\times \frac{5}{2}-\frac{3}{4}\left(-2\right)z$$

Multiply -\frac{3}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{58}{15}-7x+\frac{35}{27}z+\frac{-3\times 5}{4\times 2}-\frac{3}{4}\left(-2\right)z$$

Do the multiplications in the fraction \frac{-3\times 5}{4\times 2}.

$$\frac{58}{15}-7x+\frac{35}{27}z+\frac{-15}{8}-\frac{3}{4}\left(-2\right)z$$

Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{15}{8}-\frac{3}{4}\left(-2\right)z$$

Express -\frac{3}{4}\left(-2\right) as a single fraction.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{15}{8}+\frac{-3\left(-2\right)}{4}z$$

Multiply -3 and -2 to get 6.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{15}{8}+\frac{6}{4}z$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{15}{8}+\frac{3}{2}z$$

Least common multiple of 15 and 8 is 120. Convert \frac{58}{15} and \frac{15}{8} to fractions with denominator 120.

$$\frac{464}{120}-7x+\frac{35}{27}z-\frac{225}{120}+\frac{3}{2}z$$

Since \frac{464}{120} and \frac{225}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{464-225}{120}-7x+\frac{35}{27}z+\frac{3}{2}z$$

Subtract 225 from 464 to get 239.

$$\frac{239}{120}-7x+\frac{35}{27}z+\frac{3}{2}z$$

Combine \frac{35}{27}z and \frac{3}{2}z to get \frac{151}{54}z.

$$\frac{239}{120}-7x+\frac{151}{54}z$$

Expand

$$\frac{151z}{54}-7x+\frac{239}{120}$$

Solution Steps

Use the distributive property to multiply \frac{7}{9} by 6-9x+\frac{5}{3}z.

$$-\frac{4}{5}+\frac{7}{9}\times 6+\frac{7}{9}\left(-9\right)x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Express \frac{7}{9}\times 6 as a single fraction.

$$-\frac{4}{5}+\frac{7\times 6}{9}+\frac{7}{9}\left(-9\right)x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Multiply 7 and 6 to get 42.

$$-\frac{4}{5}+\frac{42}{9}+\frac{7}{9}\left(-9\right)x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Reduce the fraction \frac{42}{9} to lowest terms by extracting and canceling out 3.

$$-\frac{4}{5}+\frac{14}{3}+\frac{7}{9}\left(-9\right)x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Express \frac{7}{9}\left(-9\right) as a single fraction.

$$-\frac{4}{5}+\frac{14}{3}+\frac{7\left(-9\right)}{9}x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Multiply 7 and -9 to get -63.

$$-\frac{4}{5}+\frac{14}{3}+\frac{-63}{9}x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Divide -63 by 9 to get -7.

$$-\frac{4}{5}+\frac{14}{3}-7x+\frac{7}{9}\times \frac{5}{3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Multiply \frac{7}{9} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{4}{5}+\frac{14}{3}-7x+\frac{7\times 5}{9\times 3}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Do the multiplications in the fraction \frac{7\times 5}{9\times 3}.

$$-\frac{4}{5}+\frac{14}{3}-7x+\frac{35}{27}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Least common multiple of 5 and 3 is 15. Convert -\frac{4}{5} and \frac{14}{3} to fractions with denominator 15.

$$-\frac{12}{15}+\frac{70}{15}-7x+\frac{35}{27}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Since -\frac{12}{15} and \frac{70}{15} have the same denominator, add them by adding their numerators.

$$\frac{-12+70}{15}-7x+\frac{35}{27}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Add -12 and 70 to get 58.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{3}{4}\left(\frac{5}{2}-2z\right)$$

Use the distributive property to multiply -\frac{3}{4} by \frac{5}{2}-2z.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{3}{4}\times \frac{5}{2}-\frac{3}{4}\left(-2\right)z$$

Multiply -\frac{3}{4} times \frac{5}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{58}{15}-7x+\frac{35}{27}z+\frac{-3\times 5}{4\times 2}-\frac{3}{4}\left(-2\right)z$$

Do the multiplications in the fraction \frac{-3\times 5}{4\times 2}.

$$\frac{58}{15}-7x+\frac{35}{27}z+\frac{-15}{8}-\frac{3}{4}\left(-2\right)z$$

Fraction \frac{-15}{8} can be rewritten as -\frac{15}{8} by extracting the negative sign.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{15}{8}-\frac{3}{4}\left(-2\right)z$$

Express -\frac{3}{4}\left(-2\right) as a single fraction.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{15}{8}+\frac{-3\left(-2\right)}{4}z$$

Multiply -3 and -2 to get 6.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{15}{8}+\frac{6}{4}z$$

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

$$\frac{58}{15}-7x+\frac{35}{27}z-\frac{15}{8}+\frac{3}{2}z$$

Least common multiple of 15 and 8 is 120. Convert \frac{58}{15} and \frac{15}{8} to fractions with denominator 120.

$$\frac{464}{120}-7x+\frac{35}{27}z-\frac{225}{120}+\frac{3}{2}z$$

Since \frac{464}{120} and \frac{225}{120} have the same denominator, subtract them by subtracting their numerators.

$$\frac{464-225}{120}-7x+\frac{35}{27}z+\frac{3}{2}z$$

Subtract 225 from 464 to get 239.

$$\frac{239}{120}-7x+\frac{35}{27}z+\frac{3}{2}z$$

Combine \frac{35}{27}z and \frac{3}{2}z to get \frac{151}{54}z.

$$\frac{239}{120}-7x+\frac{151}{54}z$$