Algebra Examples

$2 a = b - c (\frac{b}{3} - 4)$

Step 1

Rewrite the equation as $b - c (\frac{b}{3} - 4) = 2 a$ .

$b - c (\frac{b}{3} - 4) = 2 a$

Step 2

Simplify each term.

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Step 2.1

Apply the distributive property.

$b - c \frac{b}{3} - c \cdot - 4 = 2 a$

Step 2.2

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

$b - \frac{b c}{3} - c \cdot - 4 = 2 a$

Step 2.3

Multiply $- 4$ by $- 1$ .

$b - \frac{b c}{3} + 4 c = 2 a$

Step 3

Subtract $4 c$ from both sides of the equation.

$b - \frac{b c}{3} = 2 a - 4 c$

Step 4

Factor $b$ out of $b - \frac{b c}{3}$ .

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Step 4.1

Factor $b$ out of $b^{1}$ .

$b \cdot 1 - \frac{b c}{3} = 2 a - 4 c$

Step 4.2

Factor $b$ out of $- \frac{b c}{3}$ .

$b \cdot 1 + b (- \frac{c}{3}) = 2 a - 4 c$

Step 4.3

Factor $b$ out of $b \cdot 1 + b (- \frac{c}{3})$ .

$b (1 - \frac{c}{3}) = 2 a - 4 c$

Step 5

Divide each term in $b (1 - \frac{c}{3}) = 2 a - 4 c$ by $1 - \frac{c}{3}$ and simplify.

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Step 5.1

Divide each term in $b (1 - \frac{c}{3}) = 2 a - 4 c$ by $1 - \frac{c}{3}$ .

$\frac{b (1 - \frac{c}{3})}{1 - \frac{c}{3}} = \frac{2 a}{1 - \frac{c}{3}} + \frac{- 4 c}{1 - \frac{c}{3}}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $1 - \frac{c}{3}$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{b (1 - \frac{c}{3})}{1 - \frac{c}{3}} = \frac{2 a}{1 - \frac{c}{3}} + \frac{- 4 c}{1 - \frac{c}{3}}$

Step 5.2.1.2

Divide $b$ by $1$ .

$b = \frac{2 a}{1 - \frac{c}{3}} + \frac{- 4 c}{1 - \frac{c}{3}}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Combine the numerators over the common denominator.

$b = \frac{2 a - 4 c}{1 - \frac{c}{3}}$

Step 5.3.2

Multiply the numerator and denominator of the fraction by $3$ .

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Step 5.3.2.1

Multiply $\frac{2 a - 4 c}{1 - \frac{c}{3}}$ by $\frac{3}{3}$ .

$b = \frac{3}{3} \cdot \frac{2 a - 4 c}{1 - \frac{c}{3}}$

Step 5.3.2.2

Combine.

$b = \frac{3 (2 a - 4 c)}{3 (1 - \frac{c}{3})}$

Step 5.3.3

Apply the distributive property.

$b = \frac{3 (2 a) + 3 (- 4 c)}{3 \cdot 1 + 3 (- \frac{c}{3})}$

Step 5.3.4

Cancel the common factor of $3$ .

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Step 5.3.4.1

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

$b = \frac{3 (2 a) + 3 (- 4 c)}{3 \cdot 1 + 3 \frac{- c}{3}}$

Step 5.3.4.2

Cancel the common factor.

$b = \frac{3 (2 a) + 3 (- 4 c)}{3 \cdot 1 + 3 \frac{- c}{3}}$

Step 5.3.4.3

Rewrite the expression.

$b = \frac{3 (2 a) + 3 (- 4 c)}{3 \cdot 1 - c}$

Step 5.3.5

Simplify the numerator.

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Step 5.3.5.1

Factor $3$ out of $3 \cdot 2 a + 3 (- 4 c)$ .

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Step 5.3.5.1.1

Factor $3$ out of $3 \cdot 2 a$ .

$b = \frac{3 (2 a) + 3 (- 4 c)}{3 \cdot 1 - c}$

Step 5.3.5.1.2

Factor $3$ out of $3 (2 a) + 3 (- 4 c)$ .

$b = \frac{3 (2 a - 4 c)}{3 \cdot 1 - c}$

Step 5.3.5.2

Factor $2$ out of $2 a - 4 c$ .

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Step 5.3.5.2.1

Factor $2$ out of $2 a$ .

$b = \frac{3 (2 (a) - 4 c)}{3 \cdot 1 - c}$

Step 5.3.5.2.2

Factor $2$ out of $- 4 c$ .

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

Step 5.3.5.2.3

Factor $2$ out of $2 (a) + 2 (- 2 c)$ .

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

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

Step 5.3.5.3

Multiply $3$ by $2$ .

$b = \frac{6 (a - 2 c)}{3 \cdot 1 - c}$

Step 5.3.6

Multiply $3$ by $1$ .

$b = \frac{6 (a - 2 c)}{3 - c}$