Solve 2x-12/8=-2x+2/2-x+6/4

$$\frac { 2 x - 12 } { 8 } = \frac { - 2 x + 2 } { 2 } - \frac { x + 6 } { 4 }$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 8, the least common multiple of 8,2,4.

$$2x-12=4\left(-2x+2\right)-2\left(x+6\right)$$

Use the distributive property to multiply 4 by -2x+2.

$$2x-12=-8x+8-2\left(x+6\right)$$

Use the distributive property to multiply -2 by x+6.

$$2x-12=-8x+8-2x-12$$

Combine -8x and -2x to get -10x.

$$2x-12=-10x+8-12$$

Subtract 12 from 8 to get -4.

$$2x-12=-10x-4$$

Add 10x to both sides.

$$2x-12+10x=-4$$

Combine 2x and 10x to get 12x.

$$12x-12=-4$$

Add 12 to both sides.

$$12x=-4+12$$

Add -4 and 12 to get 8.

$$12x=8$$

Divide both sides by 12.

$$x=\frac{8}{12}$$

Reduce the fraction \frac{8}{12} to lowest terms by extracting and canceling out 4.

$$x=\frac{2}{3}$$