Solve for c a=1/9(b+c-d)

$a = \frac{1}{9} (b + c - d)$

Rewrite the equation as $\frac{1}{9} \cdot (b + c - d) = a$ .

$\frac{1}{9} \cdot (b + c - d) = a$

Multiply both sides of the equation by $9$ .

$9 (\frac{1}{9} \cdot (b + c - d)) = 9 a$

Simplify the left side.

Simplify $9 (\frac{1}{9} \cdot (b + c - d))$ .

Apply the distributive property.

$9 (\frac{1}{9} b + \frac{1}{9} c + \frac{1}{9} (- d)) = 9 a$

Simplify.

Combine $\frac{1}{9}$ and $b$ .

$9 (\frac{b}{9} + \frac{1}{9} c + \frac{1}{9} (- d)) = 9 a$

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

$9 (\frac{b}{9} + \frac{c}{9} + \frac{1}{9} (- d)) = 9 a$

Combine $\frac{1}{9}$ and $d$ .

$9 (\frac{b}{9} + \frac{c}{9} - \frac{d}{9}) = 9 a$

Apply the distributive property.

$9 \frac{b}{9} + 9 \frac{c}{9} + 9 (- \frac{d}{9}) = 9 a$

Simplify.

Cancel the common factor of $9$ .

Cancel the common factor.

$9 \frac{b}{9} + 9 \frac{c}{9} + 9 (- \frac{d}{9}) = 9 a$

Rewrite the expression.

$b + 9 \frac{c}{9} + 9 (- \frac{d}{9}) = 9 a$

Cancel the common factor of $9$ .

Cancel the common factor.

$b + 9 \frac{c}{9} + 9 (- \frac{d}{9}) = 9 a$

Rewrite the expression.

$b + c + 9 (- \frac{d}{9}) = 9 a$

Cancel the common factor of $9$ .

Move the leading negative in $- \frac{d}{9}$ into the numerator.

$b + c + 9 \frac{- d}{9} = 9 a$

Cancel the common factor.

$b + c + 9 \frac{- d}{9} = 9 a$

Rewrite the expression.

$b + c - d = 9 a$

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

Subtract $b$ from both sides of the equation.

$c - d = 9 a - b$

Add $d$ to both sides of the equation.

$c = 9 a - b + d$