Solve for c a=2/3(b+c)

$a = \frac{2}{3} (b + c)$

Rewrite the equation as $\frac{2}{3} \cdot (b + c) = a$ .

$\frac{2}{3} \cdot (b + c) = a$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} (\frac{2}{3} \cdot (b + c)) = \frac{3}{2} a$

Simplify both sides of the equation.

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Simplify the left side.

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Simplify $\frac{3}{2} (\frac{2}{3} \cdot (b + c))$ .

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Apply the distributive property.

$\frac{3}{2} (\frac{2}{3} b + \frac{2}{3} c) = \frac{3}{2} a$

Combine $\frac{2}{3}$ and $b$ .

$\frac{3}{2} (\frac{2 b}{3} + \frac{2}{3} c) = \frac{3}{2} a$

Combine $\frac{2}{3}$ and $c$ .

$\frac{3}{2} (\frac{2 b}{3} + \frac{2 c}{3}) = \frac{3}{2} a$

Apply the distributive property.

$\frac{3}{2} \cdot \frac{2 b}{3} + \frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} a$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 b}{3} + \frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} a$

Rewrite the expression.

$\frac{1}{2} (2 b) + \frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} a$

Cancel the common factor of $2$ .

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Factor $2$ out of $2 b$ .

$\frac{1}{2} (2 (b)) + \frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} a$

Cancel the common factor.

$\frac{1}{2} (2 b) + \frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} a$

Rewrite the expression.

$b + \frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} a$

Cancel the common factor of $3$ .

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Cancel the common factor.

$b + \frac{3}{2} \cdot \frac{2 c}{3} = \frac{3}{2} a$

Rewrite the expression.

$b + \frac{1}{2} (2 c) = \frac{3}{2} a$

Cancel the common factor of $2$ .

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Factor $2$ out of $2 c$ .

$b + \frac{1}{2} (2 (c)) = \frac{3}{2} a$

Cancel the common factor.

$b + \frac{1}{2} (2 c) = \frac{3}{2} a$

Rewrite the expression.

$b + c = \frac{3}{2} a$

Simplify the right side.

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Combine $\frac{3}{2}$ and $a$ .

$b + c = \frac{3 a}{2}$

Subtract $b$ from both sides of the equation.

$c = \frac{3 a}{2} - b$