Solve x-5/8+x-7/8=x+6/2-x+4/2-frac{x+6}{4}

$$\frac { x - 5 } { 8 } + \frac { x - 7 } { 8 } = \frac { x + 6 } { 2 } - \frac { x + 4 } { 2 } - \frac { x + 6 } { 4 }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

$$x-5+x-7=4\left(x+6\right)-4\left(x+4\right)-2\left(x+6\right)$$

Combine x and x to get 2x.

$$2x-5-7=4\left(x+6\right)-4\left(x+4\right)-2\left(x+6\right)$$

Subtract 7 from -5 to get -12.

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

Use the distributive property to multiply 4 by x+6.

$$2x-12=4x+24-4\left(x+4\right)-2\left(x+6\right)$$

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

$$2x-12=4x+24-4x-16-2\left(x+6\right)$$

Combine 4x and -4x to get 0.

$$2x-12=24-16-2\left(x+6\right)$$

Subtract 16 from 24 to get 8.

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

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

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

Subtract 12 from 8 to get -4.

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

Add 2x to both sides.

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

Combine 2x and 2x to get 4x.

$$4x-12=-4$$

Add 12 to both sides.

$$4x=-4+12$$

Add -4 and 12 to get 8.

$$4x=8$$

Divide both sides by 4.

$$x=\frac{8}{4}$$

Divide 8 by 4 to get 2.

$$x=2$$