Solve (10)7/6(3x-9y)-4/3(4+5x)

$$( 10 ) \frac { 7 } { 6 } ( 3 x - 9 y ) - \frac { 4 } { 3 } ( 4 + 5 x )$$

Evaluate

$$\frac{85x}{3}-105y-\frac{16}{3}$$

Solution Steps

Express 10\times \frac{7}{6} as a single fraction.

$$\frac{10\times 7}{6}\left(3x-9y\right)-\frac{4}{3}\left(4+5x\right)$$

Multiply 10 and 7 to get 70.

$$\frac{70}{6}\left(3x-9y\right)-\frac{4}{3}\left(4+5x\right)$$

Reduce the fraction \frac{70}{6} to lowest terms by extracting and canceling out 2.

$$\frac{35}{3}\left(3x-9y\right)-\frac{4}{3}\left(4+5x\right)$$

Use the distributive property to multiply \frac{35}{3} by 3x-9y.

$$\frac{35}{3}\times 3x+\frac{35}{3}\left(-9\right)y-\frac{4}{3}\left(4+5x\right)$$

Cancel out 3 and 3.

$$35x+\frac{35}{3}\left(-9\right)y-\frac{4}{3}\left(4+5x\right)$$

Express \frac{35}{3}\left(-9\right) as a single fraction.

$$35x+\frac{35\left(-9\right)}{3}y-\frac{4}{3}\left(4+5x\right)$$

Multiply 35 and -9 to get -315.

$$35x+\frac{-315}{3}y-\frac{4}{3}\left(4+5x\right)$$

Divide -315 by 3 to get -105.

$$35x-105y-\frac{4}{3}\left(4+5x\right)$$

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

$$35x-105y-\frac{4}{3}\times 4-\frac{4}{3}\times 5x$$

Express -\frac{4}{3}\times 4 as a single fraction.

$$35x-105y+\frac{-4\times 4}{3}-\frac{4}{3}\times 5x$$

Multiply -4 and 4 to get -16.

$$35x-105y+\frac{-16}{3}-\frac{4}{3}\times 5x$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$35x-105y-\frac{16}{3}-\frac{4}{3}\times 5x$$

Express -\frac{4}{3}\times 5 as a single fraction.

$$35x-105y-\frac{16}{3}+\frac{-4\times 5}{3}x$$

Multiply -4 and 5 to get -20.

$$35x-105y-\frac{16}{3}+\frac{-20}{3}x$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$35x-105y-\frac{16}{3}-\frac{20}{3}x$$

Combine 35x and -\frac{20}{3}x to get \frac{85}{3}x.

$$\frac{85}{3}x-105y-\frac{16}{3}$$

Expand

$$\frac{85x}{3}-105y-\frac{16}{3}$$

Solution Steps

Express 10\times \frac{7}{6} as a single fraction.

$$\frac{10\times 7}{6}\left(3x-9y\right)-\frac{4}{3}\left(4+5x\right)$$

Multiply 10 and 7 to get 70.

$$\frac{70}{6}\left(3x-9y\right)-\frac{4}{3}\left(4+5x\right)$$

Reduce the fraction \frac{70}{6} to lowest terms by extracting and canceling out 2.

$$\frac{35}{3}\left(3x-9y\right)-\frac{4}{3}\left(4+5x\right)$$

Use the distributive property to multiply \frac{35}{3} by 3x-9y.

$$\frac{35}{3}\times 3x+\frac{35}{3}\left(-9\right)y-\frac{4}{3}\left(4+5x\right)$$

Cancel out 3 and 3.

$$35x+\frac{35}{3}\left(-9\right)y-\frac{4}{3}\left(4+5x\right)$$

Express \frac{35}{3}\left(-9\right) as a single fraction.

$$35x+\frac{35\left(-9\right)}{3}y-\frac{4}{3}\left(4+5x\right)$$

Multiply 35 and -9 to get -315.

$$35x+\frac{-315}{3}y-\frac{4}{3}\left(4+5x\right)$$

Divide -315 by 3 to get -105.

$$35x-105y-\frac{4}{3}\left(4+5x\right)$$

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

$$35x-105y-\frac{4}{3}\times 4-\frac{4}{3}\times 5x$$

Express -\frac{4}{3}\times 4 as a single fraction.

$$35x-105y+\frac{-4\times 4}{3}-\frac{4}{3}\times 5x$$

Multiply -4 and 4 to get -16.

$$35x-105y+\frac{-16}{3}-\frac{4}{3}\times 5x$$

Fraction \frac{-16}{3} can be rewritten as -\frac{16}{3} by extracting the negative sign.

$$35x-105y-\frac{16}{3}-\frac{4}{3}\times 5x$$

Express -\frac{4}{3}\times 5 as a single fraction.

$$35x-105y-\frac{16}{3}+\frac{-4\times 5}{3}x$$

Multiply -4 and 5 to get -20.

$$35x-105y-\frac{16}{3}+\frac{-20}{3}x$$

Fraction \frac{-20}{3} can be rewritten as -\frac{20}{3} by extracting the negative sign.

$$35x-105y-\frac{16}{3}-\frac{20}{3}x$$

Combine 35x and -\frac{20}{3}x to get \frac{85}{3}x.

$$\frac{85}{3}x-105y-\frac{16}{3}$$