Solve -1/2*(8x-12)-(6-x)

$$- \frac { 1 } { 2 } \cdot ( 8 x - 12 ) - ( 6 - x )$$

Evaluate

$$-3x$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by 8x-12.

$$-\frac{1}{2}\times 8x-\frac{1}{2}\left(-12\right)-\left(6-x\right)$$

Express -\frac{1}{2}\times 8 as a single fraction.

$$\frac{-8}{2}x-\frac{1}{2}\left(-12\right)-\left(6-x\right)$$

Divide -8 by 2 to get -4.

$$-4x-\frac{1}{2}\left(-12\right)-\left(6-x\right)$$

Express -\frac{1}{2}\left(-12\right) as a single fraction.

$$-4x+\frac{-\left(-12\right)}{2}-\left(6-x\right)$$

Multiply -1 and -12 to get 12.

$$-4x+\frac{12}{2}-\left(6-x\right)$$

Divide 12 by 2 to get 6.

$$-4x+6-\left(6-x\right)$$

To find the opposite of 6-x, find the opposite of each term.

$$-4x+6-6-\left(-x\right)$$

The opposite of -x is x.

$$-4x+6-6+x$$

Subtract 6 from 6 to get 0.

$$-4x+x$$

Combine -4x and x to get -3x.

$$-3x$$

Expand

$$-3x$$

Solution Steps

Use the distributive property to multiply -\frac{1}{2} by 8x-12.

$$-\frac{1}{2}\times 8x-\frac{1}{2}\left(-12\right)-\left(6-x\right)$$

Express -\frac{1}{2}\times 8 as a single fraction.

$$\frac{-8}{2}x-\frac{1}{2}\left(-12\right)-\left(6-x\right)$$

Divide -8 by 2 to get -4.

$$-4x-\frac{1}{2}\left(-12\right)-\left(6-x\right)$$

Express -\frac{1}{2}\left(-12\right) as a single fraction.

$$-4x+\frac{-\left(-12\right)}{2}-\left(6-x\right)$$

Multiply -1 and -12 to get 12.

$$-4x+\frac{12}{2}-\left(6-x\right)$$

Divide 12 by 2 to get 6.

$$-4x+6-\left(6-x\right)$$

To find the opposite of 6-x, find the opposite of each term.

$$-4x+6-6-\left(-x\right)$$

The opposite of -x is x.

$$-4x+6-6+x$$

Subtract 6 from 6 to get 0.

$$-4x+x$$

Combine -4x and x to get -3x.

$$-3x$$