Solve 8(x-3)-(6-x)=2(x+12)-5(5-x)

$$8 ( x - 3 ) - ( 6 - x ) = 2 ( x + 12 ) - 5 ( 5 - x )$$

Solve for x

$$x = \frac{29}{2} = 14\frac{1}{2} = 14.5$$

Steps for Solving Linear Equation

Use the distributive property to multiply 8 by x-3.

$$8x-24-\left(6-x\right)=2\left(x+12\right)-5\left(5-x\right)$$

To find the opposite of 6-x, find the opposite of each term.

$$8x-24-6-\left(-x\right)=2\left(x+12\right)-5\left(5-x\right)$$

The opposite of -x is x.

$$8x-24-6+x=2\left(x+12\right)-5\left(5-x\right)$$

Subtract 6 from -24 to get -30.

$$8x-30+x=2\left(x+12\right)-5\left(5-x\right)$$

Combine 8x and x to get 9x.

$$9x-30=2\left(x+12\right)-5\left(5-x\right)$$

Use the distributive property to multiply 2 by x+12.

$$9x-30=2x+24-5\left(5-x\right)$$

Use the distributive property to multiply -5 by 5-x.

$$9x-30=2x+24-25+5x$$

Subtract 25 from 24 to get -1.

$$9x-30=2x-1+5x$$

Combine 2x and 5x to get 7x.

$$9x-30=7x-1$$

Subtract 7x from both sides.

$$9x-30-7x=-1$$

Combine 9x and -7x to get 2x.

$$2x-30=-1$$

Add 30 to both sides.

$$2x=-1+30$$

Add -1 and 30 to get 29.

$$2x=29$$

Divide both sides by 2.

$$x=\frac{29}{2}$$