Solve 2x-12/8=-2x+10/2-x+6/4

$$\frac { 2 x - 12 } { 8 } = \frac { - 2 x + 10 } { 2 } - \frac { x + 6 } { 4 }$$

Solve for x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

Steps for Solving Linear Equation

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

$$2x-12=4\left(-2x+10\right)-2\left(x+6\right)$$

Use the distributive property to multiply 4 by -2x+10.

$$2x-12=-8x+40-2\left(x+6\right)$$

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

$$2x-12=-8x+40-2x-12$$

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

$$2x-12=-10x+40-12$$

Subtract 12 from 40 to get 28.

$$2x-12=-10x+28$$

Add 10x to both sides.

$$2x-12+10x=28$$

Combine 2x and 10x to get 12x.

$$12x-12=28$$

Add 12 to both sides.

$$12x=28+12$$

Add 28 and 12 to get 40.

$$12x=40$$

Divide both sides by 12.

$$x=\frac{40}{12}$$

Reduce the fraction \frac{40}{12} to lowest terms by extracting and canceling out 4.

$$x=\frac{10}{3}$$