Solve 3(2x-4)-7(x-8)=2+3(-x+4)-(2-x)

$$3(2x-4)-7(x-8)=2+3(-x+4)-(2-x)$$

Solve for x

$$x=-32$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 2x-4.

$$6x-12-7\left(x-8\right)=2+3\left(-x+4\right)-\left(2-x\right)$$

Use the distributive property to multiply -7 by x-8.

$$6x-12-7x+56=2+3\left(-x+4\right)-\left(2-x\right)$$

Combine 6x and -7x to get -x.

$$-x-12+56=2+3\left(-x+4\right)-\left(2-x\right)$$

Add -12 and 56 to get 44.

$$-x+44=2+3\left(-x+4\right)-\left(2-x\right)$$

Use the distributive property to multiply 3 by -x+4.

$$-x+44=2+3\left(-x\right)+12-\left(2-x\right)$$

Add 2 and 12 to get 14.

$$-x+44=14+3\left(-x\right)-\left(2-x\right)$$

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

$$-x+44=14+3\left(-x\right)-2-\left(-x\right)$$

The opposite of -x is x.

$$-x+44=14+3\left(-x\right)-2+x$$

Subtract 2 from 14 to get 12.

$$-x+44=12+3\left(-x\right)+x$$

Subtract 3\left(-x\right) from both sides.

$$-x+44-3\left(-x\right)=12+x$$

Subtract x from both sides.

$$-x+44-3\left(-x\right)-x=12$$

Multiply -1 and 3 to get -3.

$$-x+44-3\left(-1\right)x-x=12$$

Multiply -3 and -1 to get 3.

$$-x+44+3x-x=12$$

Combine -x and 3x to get 2x.

$$2x+44-x=12$$

Combine 2x and -x to get x.

$$x+44=12$$

Subtract 44 from both sides.

$$x=12-44$$

Subtract 44 from 12 to get -32.

$$x=-32$$