Solve for x -6x+7(1-x)=-4(x-4)

$- 6 x + 7 (1 - x) = - 4 (x - 4)$

Simplify $- 6 x + 7 (1 - x)$ .

Simplify each term.

Apply the distributive property.

$- 6 x + 7 \cdot 1 + 7 (- x) = - 4 (x - 4)$

Multiply $7$ by $1$ .

$- 6 x + 7 + 7 (- x) = - 4 (x - 4)$

Multiply $- 1$ by $7$ .

$- 6 x + 7 - 7 x = - 4 (x - 4)$

Subtract $7 x$ from $- 6 x$ .

$- 13 x + 7 = - 4 (x - 4)$

Simplify $- 4 (x - 4)$ .

Apply the distributive property.

$- 13 x + 7 = - 4 x - 4 \cdot - 4$

Multiply $- 4$ by $- 4$ .

$- 13 x + 7 = - 4 x + 16$

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

Add $4 x$ to both sides of the equation.

$- 13 x + 7 + 4 x = 16$

Add $- 13 x$ and $4 x$ .

$- 9 x + 7 = 16$

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

Subtract $7$ from both sides of the equation.

$- 9 x = 16 - 7$

Subtract $7$ from $16$ .

$- 9 x = 9$

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

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

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

Simplify the left side.

Cancel the common factor of $- 9$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $9$ by $- 9$ .

$x = - 1$