Solve for x 11-(3x+1)=7(x-6)+2

$11 - (3 x + 1) = 7 (x - 6) + 2$

Simplify $11 - (3 x + 1)$ .

Simplify each term.

Apply the distributive property.

$11 - (3 x) - 1 \cdot 1 = 7 (x - 6) + 2$

Multiply $3$ by $- 1$ .

$11 - 3 x - 1 \cdot 1 = 7 (x - 6) + 2$

Multiply $- 1$ by $1$ .

$11 - 3 x - 1 = 7 (x - 6) + 2$

Subtract $1$ from $11$ .

$- 3 x + 10 = 7 (x - 6) + 2$

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

Simplify each term.

Apply the distributive property.

$- 3 x + 10 = 7 x + 7 \cdot - 6 + 2$

Multiply $7$ by $- 6$ .

$- 3 x + 10 = 7 x - 42 + 2$

Add $- 42$ and $2$ .

$- 3 x + 10 = 7 x - 40$

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

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

$- 3 x + 10 - 7 x = - 40$

Subtract $7 x$ from $- 3 x$ .

$- 10 x + 10 = - 40$

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

Subtract $10$ from both sides of the equation.

$- 10 x = - 40 - 10$

Subtract $10$ from $- 40$ .

$- 10 x = - 50$

Divide each term in $- 10 x = - 50$ by $- 10$ and simplify.

Divide each term in $- 10 x = - 50$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{- 50}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{- 50}{- 10}$

Divide $x$ by $1$ .

$x = \frac{- 50}{- 10}$

Simplify the right side.

Divide $- 50$ by $- 10$ .

$x = 5$