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

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

Step 1

Simplify $4 (x + 1) + x$ .

Simplify each term.

Apply the distributive property.

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

Multiply $4$ by $1$ .

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

Add $4 x$ and $x$ .

$5 x + 4 = 3 (x - 2) + 2$

Step 2

Simplify $3 (x - 2) + 2$ .

Simplify each term.

Apply the distributive property.

$5 x + 4 = 3 x + 3 \cdot - 2 + 2$

Multiply $3$ by $- 2$ .

$5 x + 4 = 3 x - 6 + 2$

Add $- 6$ and $2$ .

$5 x + 4 = 3 x - 4$

Step 3

Move all terms containing $x$ to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$5 x + 4 - 3 x = - 4$

Subtract $3 x$ from $5 x$ .

$2 x + 4 = - 4$

Step 4

Move all terms not containing $x$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$2 x = - 4 - 4$

Subtract $4$ from $- 4$ .

$2 x = - 8$

Step 5

Divide each term in $2 x = - 8$ by $2$ and simplify.

Divide each term in $2 x = - 8$ by $2$ .

$\frac{2 x}{2} = \frac{- 8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 8}{2}$

Divide $x$ by $1$ .

$x = \frac{- 8}{2}$

Simplify the right side.

Divide $- 8$ by $2$ .

$x = - 4$