Solve 1/2(4-x)=-4[-x/8+3(-x-1)]

$$\frac { 1 } { 2 } ( 4 - x ) = - 4 [ - \frac { x } { 8 } + 3 ( - x - 1 ) ]$$

Solve for x

$$x=-\frac{10}{13}\approx -0.769230769$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 2,8.

$$4\left(4-x\right)=-32\left(-\frac{x}{8}+3\left(-x-1\right)\right)$$

Use the distributive property to multiply 4 by 4-x.

$$16-4x=-32\left(-\frac{x}{8}+3\left(-x-1\right)\right)$$

Use the distributive property to multiply 3 by -x-1.

$$16-4x=-32\left(-\frac{x}{8}+3\left(-x\right)-3\right)$$

Use the distributive property to multiply -32 by -\frac{x}{8}+3\left(-x\right)-3.

$$16-4x=-32\left(-\frac{x}{8}\right)-96\left(-x\right)+96$$

Multiply -32 and -1 to get 32.

$$16-4x=32\times \frac{x}{8}-96\left(-x\right)+96$$

Multiply -96 and -1 to get 96.

$$16-4x=32\times \frac{x}{8}+96x+96$$

Cancel out 8, the greatest common factor in 32 and 8.

$$16-4x=4x+96x+96$$

Combine 4x and 96x to get 100x.

$$16-4x=100x+96$$

Subtract 100x from both sides.

$$16-4x-100x=96$$

Combine -4x and -100x to get -104x.

$$16-104x=96$$

Subtract 16 from both sides.

$$-104x=96-16$$

Subtract 16 from 96 to get 80.

$$-104x=80$$

Divide both sides by -104.

$$x=\frac{80}{-104}$$

Reduce the fraction \frac{80}{-104} to lowest terms by extracting and canceling out 8.

$$x=-\frac{10}{13}$$