Solve 1/5(5x+25)-1/4(12x-12)

$$\frac { 1 } { 5 } ( 5 x + 25 ) - \frac { 1 } { 4 } ( 12 x - 12 )$$

Evaluate

$$8-2x$$

Solution Steps

Use the distributive property to multiply \frac{1}{5} by 5x+25.

$$\frac{1}{5}\times 5x+\frac{1}{5}\times 25-\frac{1}{4}\left(12x-12\right)$$

Cancel out 5 and 5.

$$x+\frac{1}{5}\times 25-\frac{1}{4}\left(12x-12\right)$$

Multiply \frac{1}{5} and 25 to get \frac{25}{5}.

$$x+\frac{25}{5}-\frac{1}{4}\left(12x-12\right)$$

Divide 25 by 5 to get 5.

$$x+5-\frac{1}{4}\left(12x-12\right)$$

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

$$x+5-\frac{1}{4}\times 12x-\frac{1}{4}\left(-12\right)$$

Express -\frac{1}{4}\times 12 as a single fraction.

$$x+5+\frac{-12}{4}x-\frac{1}{4}\left(-12\right)$$

Divide -12 by 4 to get -3.

$$x+5-3x-\frac{1}{4}\left(-12\right)$$

Express -\frac{1}{4}\left(-12\right) as a single fraction.

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

Multiply -1 and -12 to get 12.

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

Divide 12 by 4 to get 3.

$$x+5-3x+3$$

Combine x and -3x to get -2x.

$$-2x+5+3$$

Add 5 and 3 to get 8.

$$-2x+8$$

Expand

$$8-2x$$

Solution Steps

Use the distributive property to multiply \frac{1}{5} by 5x+25.

$$\frac{1}{5}\times 5x+\frac{1}{5}\times 25-\frac{1}{4}\left(12x-12\right)$$

Cancel out 5 and 5.

$$x+\frac{1}{5}\times 25-\frac{1}{4}\left(12x-12\right)$$

Multiply \frac{1}{5} and 25 to get \frac{25}{5}.

$$x+\frac{25}{5}-\frac{1}{4}\left(12x-12\right)$$

Divide 25 by 5 to get 5.

$$x+5-\frac{1}{4}\left(12x-12\right)$$

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

$$x+5-\frac{1}{4}\times 12x-\frac{1}{4}\left(-12\right)$$

Express -\frac{1}{4}\times 12 as a single fraction.

$$x+5+\frac{-12}{4}x-\frac{1}{4}\left(-12\right)$$

Divide -12 by 4 to get -3.

$$x+5-3x-\frac{1}{4}\left(-12\right)$$

Express -\frac{1}{4}\left(-12\right) as a single fraction.

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

Multiply -1 and -12 to get 12.

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

Divide 12 by 4 to get 3.

$$x+5-3x+3$$

Combine x and -3x to get -2x.

$$-2x+5+3$$

Add 5 and 3 to get 8.

$$-2x+8$$