Solve for c (9-c)/-2=3-c

$\frac{9 - c}{- 2} = 3 - c$

Step 1

Multiply both sides by $- 2$ .

$\frac{9 - c}{- 2} \cdot - 2 = (3 - c) \cdot - 2$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{9 - c}{- 2} \cdot - 2$ .

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$\frac{9 - c}{2 (- 1)} \cdot - 2 = (3 - c) \cdot - 2$

Factor $2$ out of $- 2$ .

$\frac{9 - c}{2 \cdot - 1} \cdot (2 \cdot - 1) = (3 - c) \cdot - 2$

Cancel the common factor.

$\frac{9 - c}{2 \cdot - 1} \cdot (2 \cdot - 1) = (3 - c) \cdot - 2$

Rewrite the expression.

$\frac{9 - c}{- 1} \cdot - 1 = (3 - c) \cdot - 2$

Combine $\frac{9 - c}{- 1}$ and $- 1$ .

$\frac{(9 - c) \cdot - 1}{- 1} = (3 - c) \cdot - 2$

Simplify the expression.

Move the negative one from the denominator of $\frac{(9 - c) \cdot - 1}{- 1}$ .

$- 1 \cdot ((9 - c) \cdot - 1) = (3 - c) \cdot - 2$

Rewrite $- 1 \cdot ((9 - c) \cdot - 1)$ as $- ((9 - c) \cdot - 1)$ .

$- ((9 - c) \cdot - 1) = (3 - c) \cdot - 2$

Apply the distributive property.

$- (9 \cdot - 1 - c \cdot - 1) = (3 - c) \cdot - 2$

Multiply $9$ by $- 1$ .

$- (- 9 - c \cdot - 1) = (3 - c) \cdot - 2$

Multiply $- c \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$- (- 9 + 1 c) = (3 - c) \cdot - 2$

Multiply $c$ by $1$ .

$- (- 9 + c) = (3 - c) \cdot - 2$

Apply the distributive property.

$- - 9 - c = (3 - c) \cdot - 2$

Simplify the expression.

Multiply $- 1$ by $- 9$ .

$9 - c = (3 - c) \cdot - 2$

Reorder $9$ and $- c$ .

$- c + 9 = (3 - c) \cdot - 2$

Simplify the right side.

Simplify $(3 - c) \cdot - 2$ .

Apply the distributive property.

$- c + 9 = 3 \cdot - 2 - c \cdot - 2$

Simplify the expression.

Multiply $3$ by $- 2$ .

$- c + 9 = - 6 - c \cdot - 2$

Multiply $- 2$ by $- 1$ .

$- c + 9 = - 6 + 2 c$

Reorder $- 6$ and $2 c$ .

$- c + 9 = 2 c - 6$

Step 3

Solve for $c$ .

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

Subtract $2 c$ from both sides of the equation.

$- c + 9 - 2 c = - 6$

Subtract $2 c$ from $- c$ .

$- 3 c + 9 = - 6$

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

Subtract $9$ from both sides of the equation.

$- 3 c = - 6 - 9$

Subtract $9$ from $- 6$ .

$- 3 c = - 15$

Divide each term in $- 3 c = - 15$ by $- 3$ and simplify.

Divide each term in $- 3 c = - 15$ by $- 3$ .

$\frac{- 3 c}{- 3} = \frac{- 15}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 c}{- 3} = \frac{- 15}{- 3}$

Divide $c$ by $1$ .

$c = \frac{- 15}{- 3}$

Simplify the right side.

Divide $- 15$ by $- 3$ .

$c = 5$

Solve for c (9-c)/-2=3-c

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