Solve for x -(1+7x)-6(-7-x)=36

$- (1 + 7 x) - 6 (- 7 - x) = 36$

Step 1

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

Simplify each term.

Apply the distributive property.

$- 1 \cdot 1 - (7 x) - 6 (- 7 - x) = 36$

Multiply $- 1$ by $1$ .

$- 1 - (7 x) - 6 (- 7 - x) = 36$

Multiply $7$ by $- 1$ .

$- 1 - 7 x - 6 (- 7 - x) = 36$

Apply the distributive property.

$- 1 - 7 x - 6 \cdot - 7 - 6 (- x) = 36$

Multiply $- 6$ by $- 7$ .

$- 1 - 7 x + 42 - 6 (- x) = 36$

Multiply $- 1$ by $- 6$ .

$- 1 - 7 x + 42 + 6 x = 36$

Simplify by adding terms.

Add $- 1$ and $42$ .

$- 7 x + 41 + 6 x = 36$

Add $- 7 x$ and $6 x$ .

$- x + 41 = 36$

Step 2

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

Subtract $41$ from both sides of the equation.

$- x = 36 - 41$

Subtract $41$ from $36$ .

$- x = - 5$

Step 3

Divide each term in $- x = - 5$ by $- 1$ and simplify.

Divide each term in $- x = - 5$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 5}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 5}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 5}{- 1}$

Simplify the right side.

Divide $- 5$ by $- 1$ .

$x = 5$