Solve 1/4(12x-16)-1/8(16x-64)

$$\frac { 1 } { 4 } ( 12 x - 16 ) - \frac { 1 } { 8 } ( 16 x - 64 )$$

Evaluate

$$x+4$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 12x-16.

$$\frac{1}{4}\times 12x+\frac{1}{4}\left(-16\right)-\frac{1}{8}\left(16x-64\right)$$

Multiply \frac{1}{4} and 12 to get \frac{12}{4}.

$$\frac{12}{4}x+\frac{1}{4}\left(-16\right)-\frac{1}{8}\left(16x-64\right)$$

Divide 12 by 4 to get 3.

$$3x+\frac{1}{4}\left(-16\right)-\frac{1}{8}\left(16x-64\right)$$

Multiply \frac{1}{4} and -16 to get \frac{-16}{4}.

$$3x+\frac{-16}{4}-\frac{1}{8}\left(16x-64\right)$$

Divide -16 by 4 to get -4.

$$3x-4-\frac{1}{8}\left(16x-64\right)$$

Use the distributive property to multiply -\frac{1}{8} by 16x-64.

$$3x-4-\frac{1}{8}\times 16x-\frac{1}{8}\left(-64\right)$$

Express -\frac{1}{8}\times 16 as a single fraction.

$$3x-4+\frac{-16}{8}x-\frac{1}{8}\left(-64\right)$$

Divide -16 by 8 to get -2.

$$3x-4-2x-\frac{1}{8}\left(-64\right)$$

Express -\frac{1}{8}\left(-64\right) as a single fraction.

$$3x-4-2x+\frac{-\left(-64\right)}{8}$$

Multiply -1 and -64 to get 64.

$$3x-4-2x+\frac{64}{8}$$

Divide 64 by 8 to get 8.

$$3x-4-2x+8$$

Combine 3x and -2x to get x.

$$x-4+8$$

Add -4 and 8 to get 4.

$$x+4$$

Expand

$$x+4$$

Solution Steps

Use the distributive property to multiply \frac{1}{4} by 12x-16.

$$\frac{1}{4}\times 12x+\frac{1}{4}\left(-16\right)-\frac{1}{8}\left(16x-64\right)$$

Multiply \frac{1}{4} and 12 to get \frac{12}{4}.

$$\frac{12}{4}x+\frac{1}{4}\left(-16\right)-\frac{1}{8}\left(16x-64\right)$$

Divide 12 by 4 to get 3.

$$3x+\frac{1}{4}\left(-16\right)-\frac{1}{8}\left(16x-64\right)$$

Multiply \frac{1}{4} and -16 to get \frac{-16}{4}.

$$3x+\frac{-16}{4}-\frac{1}{8}\left(16x-64\right)$$

Divide -16 by 4 to get -4.

$$3x-4-\frac{1}{8}\left(16x-64\right)$$

Use the distributive property to multiply -\frac{1}{8} by 16x-64.

$$3x-4-\frac{1}{8}\times 16x-\frac{1}{8}\left(-64\right)$$

Express -\frac{1}{8}\times 16 as a single fraction.

$$3x-4+\frac{-16}{8}x-\frac{1}{8}\left(-64\right)$$

Divide -16 by 8 to get -2.

$$3x-4-2x-\frac{1}{8}\left(-64\right)$$

Express -\frac{1}{8}\left(-64\right) as a single fraction.

$$3x-4-2x+\frac{-\left(-64\right)}{8}$$

Multiply -1 and -64 to get 64.

$$3x-4-2x+\frac{64}{8}$$

Divide 64 by 8 to get 8.

$$3x-4-2x+8$$

Combine 3x and -2x to get x.

$$x-4+8$$

Add -4 and 8 to get 4.

$$x+4$$