Solve 4/5(5x-10)-3/4(12+4x)

$$\frac { 4 } { 5 } ( 5 x - 10 ) - \frac { 3 } { 4 } ( 12 + 4 x )$$

Evaluate

$$x-17$$

Solution Steps

Use the distributive property to multiply \frac{4}{5} by 5x-10.

$$\frac{4}{5}\times 5x+\frac{4}{5}\left(-10\right)-\frac{3}{4}\left(12+4x\right)$$

Cancel out 5 and 5.

$$4x+\frac{4}{5}\left(-10\right)-\frac{3}{4}\left(12+4x\right)$$

Express \frac{4}{5}\left(-10\right) as a single fraction.

$$4x+\frac{4\left(-10\right)}{5}-\frac{3}{4}\left(12+4x\right)$$

Multiply 4 and -10 to get -40.

$$4x+\frac{-40}{5}-\frac{3}{4}\left(12+4x\right)$$

Divide -40 by 5 to get -8.

$$4x-8-\frac{3}{4}\left(12+4x\right)$$

Use the distributive property to multiply -\frac{3}{4} by 12+4x.

$$4x-8-\frac{3}{4}\times 12-\frac{3}{4}\times 4x$$

Express -\frac{3}{4}\times 12 as a single fraction.

$$4x-8+\frac{-3\times 12}{4}-\frac{3}{4}\times 4x$$

Multiply -3 and 12 to get -36.

$$4x-8+\frac{-36}{4}-\frac{3}{4}\times 4x$$

Divide -36 by 4 to get -9.

$$4x-8-9-\frac{3}{4}\times 4x$$

Cancel out 4 and 4.

$$4x-8-9-3x$$

Subtract 9 from -8 to get -17.

$$4x-17-3x$$

Combine 4x and -3x to get x.

$$x-17$$

Expand

$$x-17$$

Solution Steps

Use the distributive property to multiply \frac{4}{5} by 5x-10.

$$\frac{4}{5}\times 5x+\frac{4}{5}\left(-10\right)-\frac{3}{4}\left(12+4x\right)$$

Cancel out 5 and 5.

$$4x+\frac{4}{5}\left(-10\right)-\frac{3}{4}\left(12+4x\right)$$

Express \frac{4}{5}\left(-10\right) as a single fraction.

$$4x+\frac{4\left(-10\right)}{5}-\frac{3}{4}\left(12+4x\right)$$

Multiply 4 and -10 to get -40.

$$4x+\frac{-40}{5}-\frac{3}{4}\left(12+4x\right)$$

Divide -40 by 5 to get -8.

$$4x-8-\frac{3}{4}\left(12+4x\right)$$

Use the distributive property to multiply -\frac{3}{4} by 12+4x.

$$4x-8-\frac{3}{4}\times 12-\frac{3}{4}\times 4x$$

Express -\frac{3}{4}\times 12 as a single fraction.

$$4x-8+\frac{-3\times 12}{4}-\frac{3}{4}\times 4x$$

Multiply -3 and 12 to get -36.

$$4x-8+\frac{-36}{4}-\frac{3}{4}\times 4x$$

Divide -36 by 4 to get -9.

$$4x-8-9-\frac{3}{4}\times 4x$$

Cancel out 4 and 4.

$$4x-8-9-3x$$

Subtract 9 from -8 to get -17.

$$4x-17-3x$$

Combine 4x and -3x to get x.

$$x-17$$