Algebra Examples

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

Step 1

Rewrite the equation as $- 3 (a + b - \frac{1}{3} c) = A$ .

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

Step 2

Simplify $- 3 (a + b - \frac{1}{3} c)$ .

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Step 2.1

Combine $c$ and $\frac{1}{3}$ .

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

Step 2.2

Apply the distributive property.

$- 3 a - 3 b - 3 (- \frac{c}{3}) = A$

Step 2.3

Simplify.

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Step 2.3.1

Cancel the common factor of $3$ .

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Step 2.3.1.1

Move the leading negative in $- \frac{c}{3}$ into the numerator.

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

Step 2.3.1.2

Factor $3$ out of $- 3$ .

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

Step 2.3.1.3

Cancel the common factor.

$- 3 a - 3 b + 3 \cdot - 1 \frac{- c}{3} = A$

Step 2.3.1.4

Rewrite the expression.

$- 3 a - 3 b - 1 (- c) = A$

Step 2.3.2

Multiply $- 1$ by $- 1$ .

$- 3 a - 3 b + 1 c = A$

Step 2.3.3

Multiply $c$ by $1$ .

$- 3 a - 3 b + c = A$

Step 3

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

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Step 3.1

Add $3 a$ to both sides of the equation.

$- 3 b + c = A + 3 a$

Step 3.2

Add $3 b$ to both sides of the equation.

$c = A + 3 a + 3 b$