Solve 3(x-2)+4(2-x)=x+2(x+1)

$$3 ( x - 2 ) + 4 ( 2 - x ) = x + 2 ( x + 1 )$$

Solve for x

$$x=0$$

Steps for Solving Linear Equation

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

$$3x-6+4\left(2-x\right)=x+2\left(x+1\right)$$

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

$$3x-6+8-4x=x+2\left(x+1\right)$$

Add -6 and 8 to get 2.

$$3x+2-4x=x+2\left(x+1\right)$$

Combine 3x and -4x to get -x.

$$-x+2=x+2\left(x+1\right)$$

Use the distributive property to multiply 2 by x+1.

$$-x+2=x+2x+2$$

Combine x and 2x to get 3x.

$$-x+2=3x+2$$

Subtract 3x from both sides.

$$-x+2-3x=2$$

Combine -x and -3x to get -4x.

$$-4x+2=2$$

Subtract 2 from both sides.

$$-4x=2-2$$

Subtract 2 from 2 to get 0.

$$-4x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since -4 is not equal to 0, x must be equal to 0.

$$x=0$$