Solve for x 7(3x-1)-(x+5)=-52

$7 (3 x - 1) - (x + 5) = - 52$

Simplify $7 (3 x - 1) - (x + 5)$ .

Simplify each term.

Apply the distributive property.

$7 (3 x) + 7 \cdot - 1 - (x + 5) = - 52$

Multiply $3$ by $7$ .

$21 x + 7 \cdot - 1 - (x + 5) = - 52$

Multiply $7$ by $- 1$ .

$21 x - 7 - (x + 5) = - 52$

Apply the distributive property.

$21 x - 7 - x - 1 \cdot 5 = - 52$

Multiply $- 1$ by $5$ .

$21 x - 7 - x - 5 = - 52$

Simplify by adding terms.

Subtract $x$ from $21 x$ .

$20 x - 7 - 5 = - 52$

Subtract $5$ from $- 7$ .

$20 x - 12 = - 52$

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

Add $12$ to both sides of the equation.

$20 x = - 52 + 12$

Add $- 52$ and $12$ .

$20 x = - 40$

Divide each term in $20 x = - 40$ by $20$ and simplify.

Divide each term in $20 x = - 40$ by $20$ .

$\frac{20 x}{20} = \frac{- 40}{20}$

Simplify the left side.

Cancel the common factor of $20$ .

Cancel the common factor.

$\frac{20 x}{20} = \frac{- 40}{20}$

Divide $x$ by $1$ .

$x = \frac{- 40}{20}$

Simplify the right side.

Divide $- 40$ by $20$ .

$x = - 2$