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

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

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.

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

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

$$x-5+4x+16=4\left(x+6\right)-\left(x-7\right)-2\left(x+6\right)$$

Combine x and 4x to get 5x.

$$5x-5+16=4\left(x+6\right)-\left(x-7\right)-2\left(x+6\right)$$

Add -5 and 16 to get 11.

$$5x+11=4\left(x+6\right)-\left(x-7\right)-2\left(x+6\right)$$

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

$$5x+11=4x+24-\left(x-7\right)-2\left(x+6\right)$$

To find the opposite of x-7, find the opposite of each term.

$$5x+11=4x+24-x-\left(-7\right)-2\left(x+6\right)$$

The opposite of -7 is 7.

$$5x+11=4x+24-x+7-2\left(x+6\right)$$

Combine 4x and -x to get 3x.

$$5x+11=3x+24+7-2\left(x+6\right)$$

Add 24 and 7 to get 31.

$$5x+11=3x+31-2\left(x+6\right)$$

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

$$5x+11=3x+31-2x-12$$

Combine 3x and -2x to get x.

$$5x+11=x+31-12$$

Subtract 12 from 31 to get 19.

$$5x+11=x+19$$

Subtract x from both sides.

$$5x+11-x=19$$

Combine 5x and -x to get 4x.

$$4x+11=19$$

Subtract 11 from both sides.

$$4x=19-11$$

Subtract 11 from 19 to get 8.

$$4x=8$$

Divide both sides by 4.

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

Divide 8 by 4 to get 2.

$$x=2$$