Solve for k 1/2(10k-16)+11=-2

$\frac{1}{2} (10 k - 16) + 11 = - 2$

Simplify $\frac{1}{2} \cdot (10 k - 16) + 11$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{2} (10 k) + \frac{1}{2} \cdot - 16 + 11 = - 2$

Cancel the common factor of $2$ .

Factor $2$ out of $10 k$ .

$\frac{1}{2} (2 (5 k)) + \frac{1}{2} \cdot - 16 + 11 = - 2$

Cancel the common factor.

$\frac{1}{2} (2 (5 k)) + \frac{1}{2} \cdot - 16 + 11 = - 2$

Rewrite the expression.

$5 k + \frac{1}{2} \cdot - 16 + 11 = - 2$

Cancel the common factor of $2$ .

Factor $2$ out of $- 16$ .

$5 k + \frac{1}{2} \cdot (2 (- 8)) + 11 = - 2$

Cancel the common factor.

$5 k + \frac{1}{2} \cdot (2 \cdot - 8) + 11 = - 2$

Rewrite the expression.

$5 k - 8 + 11 = - 2$

Add $- 8$ and $11$ .

$5 k + 3 = - 2$

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

Subtract $3$ from both sides of the equation.

$5 k = - 2 - 3$

Subtract $3$ from $- 2$ .

$5 k = - 5$

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

Divide each term in $5 k = - 5$ by $5$ .

$\frac{5 k}{5} = \frac{- 5}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 k}{5} = \frac{- 5}{5}$

Divide $k$ by $1$ .

$k = \frac{- 5}{5}$

Simplify the right side.

Divide $- 5$ by $5$ .

$k = - 1$