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

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

Solve for x

$$x = \frac{29}{3} = 9\frac{2}{3} \approx 9.666666667$$

Steps for Solving Linear Equation

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

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

To find the opposite of 6-2x, find the opposite of each term.

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

The opposite of -2x is 2x.

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

Subtract 6 from -24 to get -30.

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

Combine 8x and 2x to get 10x.

$$10x-30=2\left(x+12\right)-5\left(5-x\right)$$

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

$$10x-30=2x+24-5\left(5-x\right)$$

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

$$10x-30=2x+24-25+5x$$

Subtract 25 from 24 to get -1.

$$10x-30=2x-1+5x$$

Combine 2x and 5x to get 7x.

$$10x-30=7x-1$$

Subtract 7x from both sides.

$$10x-30-7x=-1$$

Combine 10x and -7x to get 3x.

$$3x-30=-1$$

Add 30 to both sides.

$$3x=-1+30$$

Add -1 and 30 to get 29.

$$3x=29$$

Divide both sides by 3.

$$x=\frac{29}{3}$$