Solve x-4/8+x+1/2=x+7/2-x-5/8-frac{x+6}{4}

$$\frac { x - 4 } { 8 } + \frac { x + 1 } { 2 } = \frac { x + 7 } { 2 } - \frac { x - 5 } { 8 } - \frac { x + 6 } { 4 }$$

Solve for x

$$x = \frac{21}{4} = 5\frac{1}{4} = 5.25$$

Steps for Solving Linear Equation

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

$$x-4+4\left(x+1\right)=4\left(x+7\right)-\left(x-5\right)-2\left(x+6\right)$$

Use the distributive property to multiply 4 by x+1.

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

Combine x and 4x to get 5x.

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

Add -4 and 4 to get 0.

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

Use the distributive property to multiply 4 by x+7.

$$5x=4x+28-\left(x-5\right)-2\left(x+6\right)$$

To find the opposite of x-5, find the opposite of each term.

$$5x=4x+28-x-\left(-5\right)-2\left(x+6\right)$$

The opposite of -5 is 5.

$$5x=4x+28-x+5-2\left(x+6\right)$$

Combine 4x and -x to get 3x.

$$5x=3x+28+5-2\left(x+6\right)$$

Add 28 and 5 to get 33.

$$5x=3x+33-2\left(x+6\right)$$

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

$$5x=3x+33-2x-12$$

Combine 3x and -2x to get x.

$$5x=x+33-12$$

Subtract 12 from 33 to get 21.

$$5x=x+21$$

Subtract x from both sides.

$$5x-x=21$$

Combine 5x and -x to get 4x.

$$4x=21$$

Divide both sides by 4.

$$x=\frac{21}{4}$$