Solve for k 9(11-k)=3(3k-9)

$9 (11 - k) = 3 (3 k - 9)$

Step 1

Simplify $9 (11 - k)$ .

Rewrite.

$0 + 0 + 9 (11 - k) = 3 (3 k - 9)$

Simplify by adding zeros.

$9 (11 - k) = 3 (3 k - 9)$

Apply the distributive property.

$9 \cdot 11 + 9 (- k) = 3 (3 k - 9)$

Multiply.

Multiply $9$ by $11$ .

$99 + 9 (- k) = 3 (3 k - 9)$

Multiply $- 1$ by $9$ .

$99 - 9 k = 3 (3 k - 9)$

Step 2

Simplify $3 (3 k - 9)$ .

Apply the distributive property.

$99 - 9 k = 3 (3 k) + 3 \cdot - 9$

Multiply.

Multiply $3$ by $3$ .

$99 - 9 k = 9 k + 3 \cdot - 9$

Multiply $3$ by $- 9$ .

$99 - 9 k = 9 k - 27$

Step 3

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

Subtract $9 k$ from both sides of the equation.

$99 - 9 k - 9 k = - 27$

Subtract $9 k$ from $- 9 k$ .

$99 - 18 k = - 27$

Step 4

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

Subtract $99$ from both sides of the equation.

$- 18 k = - 27 - 99$

Subtract $99$ from $- 27$ .

$- 18 k = - 126$

Step 5

Divide each term in $- 18 k = - 126$ by $- 18$ and simplify.

Divide each term in $- 18 k = - 126$ by $- 18$ .

$\frac{- 18 k}{- 18} = \frac{- 126}{- 18}$

Simplify the left side.

Cancel the common factor of $- 18$ .

Cancel the common factor.

$\frac{- 18 k}{- 18} = \frac{- 126}{- 18}$

Divide $k$ by $1$ .

$k = \frac{- 126}{- 18}$

Simplify the right side.

Divide $- 126$ by $- 18$ .

$k = 7$

Solve for k 9(11-k)=3(3k-9)

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