Algebra Examples

$\frac{2}{3} a + 6 b = c$

Step 1

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

$\frac{2 a}{3} + 6 b = c$

Step 2

Subtract $6 b$ from both sides of the equation.

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

Step 3

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

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

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{2} \cdot \frac{2 a}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

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

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 a$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{3}{2} (c - 6 b)$ .

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Step 4.2.1.1

Apply the distributive property.

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

Step 4.2.1.2

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

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

Step 4.2.1.3

Cancel the common factor of $2$ .

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Step 4.2.1.3.1

Factor $2$ out of $- 6 b$ .

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

Step 4.2.1.3.2

Cancel the common factor.

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

Step 4.2.1.3.3

Rewrite the expression.

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

Step 4.2.1.4

Multiply $- 3$ by $3$ .

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

Step 5

Reorder $\frac{3 c}{2}$ and $- 9 b$ .

$a = - 9 b + \frac{3 c}{2}$