Solve for x 2x-(11(x-4)+3)=77

$2 x - (11 (x - 4) + 3) = 77$

Step 1

Simplify $2 x - (11 (x - 4) + 3)$ .

Simplify each term.

Apply the distributive property.

$2 x - (11 x + 11 \cdot - 4 + 3) = 77$

Multiply $11$ by $- 4$ .

$2 x - (11 x - 44 + 3) = 77$

Add $- 44$ and $3$ .

$2 x - (11 x - 41) = 77$

Apply the distributive property.

$2 x - (11 x) - - 41 = 77$

Multiply $11$ by $- 1$ .

$2 x - 11 x - - 41 = 77$

Multiply $- 1$ by $- 41$ .

$2 x - 11 x + 41 = 77$

Subtract $11 x$ from $2 x$ .

$- 9 x + 41 = 77$

Step 2

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

Subtract $41$ from both sides of the equation.

$- 9 x = 77 - 41$

Subtract $41$ from $77$ .

$- 9 x = 36$

Step 3

Divide each term in $- 9 x = 36$ by $- 9$ and simplify.

Divide each term in $- 9 x = 36$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{36}{- 9}$

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{36}{- 9}$

Divide $x$ by $1$ .

$x = \frac{36}{- 9}$

Simplify the right side.

Divide $36$ by $- 9$ .

$x = - 4$