Solve for x 3(x+2)+2x=7(x-1)+9

$3 (x + 2) + 2 x = 7 (x - 1) + 9$

Step 1

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

Simplify each term.

Apply the distributive property.

$3 x + 3 \cdot 2 + 2 x = 7 (x - 1) + 9$

Multiply $3$ by $2$ .

$3 x + 6 + 2 x = 7 (x - 1) + 9$

Add $3 x$ and $2 x$ .

$5 x + 6 = 7 (x - 1) + 9$

Step 2

Simplify $7 (x - 1) + 9$ .

Simplify each term.

Apply the distributive property.

$5 x + 6 = 7 x + 7 \cdot - 1 + 9$

Multiply $7$ by $- 1$ .

$5 x + 6 = 7 x - 7 + 9$

Add $- 7$ and $9$ .

$5 x + 6 = 7 x + 2$

Step 3

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

Subtract $7 x$ from both sides of the equation.

$5 x + 6 - 7 x = 2$

Subtract $7 x$ from $5 x$ .

$- 2 x + 6 = 2$

Step 4

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

Subtract $6$ from both sides of the equation.

$- 2 x = 2 - 6$

Subtract $6$ from $2$ .

$- 2 x = - 4$

Step 5

Divide each term in $- 2 x = - 4$ by $- 2$ and simplify.

Divide each term in $- 2 x = - 4$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 4}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- 4}{- 2}$

Simplify the right side.

Divide $- 4$ by $- 2$ .

$x = 2$