Solve 1/2(2x+8)-1/5(10x-5)

$$\frac{ 1 }{ 2 } (2x+8)- \frac{ 1 }{ 5 } (10x-5)$$

Evaluate

$$5-x$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x+8.

$$\frac{1}{2}\times 2x+\frac{1}{2}\times 8-\frac{1}{5}\left(10x-5\right)$$

Cancel out 2 and 2.

$$x+\frac{1}{2}\times 8-\frac{1}{5}\left(10x-5\right)$$

Multiply \frac{1}{2} and 8 to get \frac{8}{2}.

$$x+\frac{8}{2}-\frac{1}{5}\left(10x-5\right)$$

Divide 8 by 2 to get 4.

$$x+4-\frac{1}{5}\left(10x-5\right)$$

Use the distributive property to multiply -\frac{1}{5} by 10x-5.

$$x+4-\frac{1}{5}\times 10x-\frac{1}{5}\left(-5\right)$$

Express -\frac{1}{5}\times 10 as a single fraction.

$$x+4+\frac{-10}{5}x-\frac{1}{5}\left(-5\right)$$

Divide -10 by 5 to get -2.

$$x+4-2x-\frac{1}{5}\left(-5\right)$$

Express -\frac{1}{5}\left(-5\right) as a single fraction.

$$x+4-2x+\frac{-\left(-5\right)}{5}$$

Multiply -1 and -5 to get 5.

$$x+4-2x+\frac{5}{5}$$

Divide 5 by 5 to get 1.

$$x+4-2x+1$$

Combine x and -2x to get -x.

$$-x+4+1$$

Add 4 and 1 to get 5.

$$-x+5$$

Expand

$$5-x$$

Solution Steps

Use the distributive property to multiply \frac{1}{2} by 2x+8.

$$\frac{1}{2}\times 2x+\frac{1}{2}\times 8-\frac{1}{5}\left(10x-5\right)$$

Cancel out 2 and 2.

$$x+\frac{1}{2}\times 8-\frac{1}{5}\left(10x-5\right)$$

Multiply \frac{1}{2} and 8 to get \frac{8}{2}.

$$x+\frac{8}{2}-\frac{1}{5}\left(10x-5\right)$$

Divide 8 by 2 to get 4.

$$x+4-\frac{1}{5}\left(10x-5\right)$$

Use the distributive property to multiply -\frac{1}{5} by 10x-5.

$$x+4-\frac{1}{5}\times 10x-\frac{1}{5}\left(-5\right)$$

Express -\frac{1}{5}\times 10 as a single fraction.

$$x+4+\frac{-10}{5}x-\frac{1}{5}\left(-5\right)$$

Divide -10 by 5 to get -2.

$$x+4-2x-\frac{1}{5}\left(-5\right)$$

Express -\frac{1}{5}\left(-5\right) as a single fraction.

$$x+4-2x+\frac{-\left(-5\right)}{5}$$

Multiply -1 and -5 to get 5.

$$x+4-2x+\frac{5}{5}$$

Divide 5 by 5 to get 1.

$$x+4-2x+1$$

Combine x and -2x to get -x.

$$-x+4+1$$

Add 4 and 1 to get 5.

$$-x+5$$