Solve for x -3(x+2)=2(x+6)+7

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

Step 1

Simplify $- 3 (x + 2)$ .

Rewrite.

$0 + 0 - 3 (x + 2) = 2 (x + 6) + 7$

Simplify by adding zeros.

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

Apply the distributive property.

$- 3 x - 3 \cdot 2 = 2 (x + 6) + 7$

Multiply $- 3$ by $2$ .

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

Step 2

Simplify $2 (x + 6) + 7$ .

Simplify each term.

Apply the distributive property.

$- 3 x - 6 = 2 x + 2 \cdot 6 + 7$

Multiply $2$ by $6$ .

$- 3 x - 6 = 2 x + 12 + 7$

Add $12$ and $7$ .

$- 3 x - 6 = 2 x + 19$

Step 3

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

Subtract $2 x$ from both sides of the equation.

$- 3 x - 6 - 2 x = 19$

Subtract $2 x$ from $- 3 x$ .

$- 5 x - 6 = 19$

Step 4

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

Add $6$ to both sides of the equation.

$- 5 x = 19 + 6$

Add $19$ and $6$ .

$- 5 x = 25$

Step 5

Divide each term in $- 5 x = 25$ by $- 5$ and simplify.

Divide each term in $- 5 x = 25$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{25}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{25}{- 5}$

Divide $x$ by $1$ .

$x = \frac{25}{- 5}$

Simplify the right side.

Divide $25$ by $- 5$ .

$x = - 5$