Solve 5(2-x)-3(x+2)=2(2x+2)-3(2+x)-3

$$5 ( 2 - x ) - 3 ( x + 2 ) = 2 ( 2 x + 2 ) - 3 ( 2 + x ) - 3$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by 2-x.

$$10-5x-3\left(x+2\right)=2\left(2x+2\right)-3\left(2+x\right)-3$$

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

$$10-5x-3x-6=2\left(2x+2\right)-3\left(2+x\right)-3$$

Combine -5x and -3x to get -8x.

$$10-8x-6=2\left(2x+2\right)-3\left(2+x\right)-3$$

Subtract 6 from 10 to get 4.

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

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

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

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

$$4-8x=4x+4-6-3x-3$$

Subtract 6 from 4 to get -2.

$$4-8x=4x-2-3x-3$$

Combine 4x and -3x to get x.

$$4-8x=x-2-3$$

Subtract 3 from -2 to get -5.

$$4-8x=x-5$$

Subtract x from both sides.

$$4-8x-x=-5$$

Combine -8x and -x to get -9x.

$$4-9x=-5$$

Subtract 4 from both sides.

$$-9x=-5-4$$

Subtract 4 from -5 to get -9.

$$-9x=-9$$

Divide both sides by -9.

$$x=\frac{-9}{-9}$$

Divide -9 by -9 to get 1.

$$x=1$$