Evaluate -7(k+5)=3k-(8k-1)

$- 7 (k + 5) = 3 k - (8 k - 1)$

Since $k$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$3 k - (8 k - 1) = - 7 (k + 5)$

Simplify $3 k - (8 k - 1)$ .

Simplify each term.

Apply the distributive property.

$3 k - (8 k) - - 1 = - 7 (k + 5)$

Multiply $8$ by $- 1$ .

$3 k - 8 k - - 1 = - 7 (k + 5)$

Multiply $- 1$ by $- 1$ .

$3 k - 8 k + 1 = - 7 (k + 5)$

Subtract $8 k$ from $3 k$ .

$- 5 k + 1 = - 7 (k + 5)$

Simplify $- 7 (k + 5)$ .

Apply the distributive property.

$- 5 k + 1 = - 7 k - 7 \cdot 5$

Multiply $- 7$ by $5$ .

$- 5 k + 1 = - 7 k - 35$

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

Add $7 k$ to both sides of the equation.

$- 5 k + 1 + 7 k = - 35$

Add $- 5 k$ and $7 k$ .

$2 k + 1 = - 35$

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

Subtract $1$ from both sides of the equation.

$2 k = - 35 - 1$

Subtract $1$ from $- 35$ .

$2 k = - 36$

Divide each term in $2 k = - 36$ by $2$ and simplify.

Divide each term in $2 k = - 36$ by $2$ .

$\frac{2 k}{2} = \frac{- 36}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 k}{2} = \frac{- 36}{2}$

Divide $k$ by $1$ .

$k = \frac{- 36}{2}$

Simplify the right side.

Divide $- 36$ by $2$ .

$k = - 18$