Solve 2(x/4+4)-4(x/2+2)=8-2x

$$2 ( \frac { x } { 4 } + 4 ) - 4 ( \frac { x } { 2 } + 2 ) = 8 - 2 x$$

Solve for x

$$x=16$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 4, the least common multiple of 4,2.

$$8\left(\frac{x}{4}+4\right)-16\left(\frac{x}{2}+2\right)=32-8x$$

Use the distributive property to multiply 8 by \frac{x}{4}+4.

$$8\times \frac{x}{4}+32-16\left(\frac{x}{2}+2\right)=32-8x$$

Cancel out 4, the greatest common factor in 8 and 4.

$$2x+32-16\left(\frac{x}{2}+2\right)=32-8x$$

Add 8x to both sides.

$$2x+32-16\left(\frac{x}{2}+2\right)+8x=32$$

Multiply both sides of the equation by 2.

$$2\left(2x+32-16\left(\frac{x}{2}+2\right)\right)+16x=64$$

Multiply both sides of the equation by 2.

$$4\left(2x+32-16\left(\frac{x}{2}+2\right)\right)+32x=128$$

Use the distributive property to multiply -16 by \frac{x}{2}+2.

$$4\left(2x+32-16\times \frac{x}{2}-32\right)+32x=128$$

Cancel out 2, the greatest common factor in 16 and 2.

$$4\left(2x+32-8x-32\right)+32x=128$$

Combine 2x and -8x to get -6x.

$$4\left(-6x+32-32\right)+32x=128$$

Subtract 32 from 32 to get 0.

$$4\left(-6\right)x+32x=128$$

Multiply 4 and -6 to get -24.

$$-24x+32x=128$$

Combine -24x and 32x to get 8x.

$$8x=128$$

Divide both sides by 8.

$$x=\frac{128}{8}$$

Divide 128 by 8 to get 16.

$$x=16$$