Algebra Examples

$\frac{2}{9} x - \frac{1}{3} = 1$

Step 1

Combine $\frac{2}{9}$ and $x$ .

$\frac{2 x}{9} - \frac{1}{3} = 1$

Step 2

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

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Step 2.1

Add $\frac{1}{3}$ to both sides of the equation.

$\frac{2 x}{9} = 1 + \frac{1}{3}$

Step 2.2

Write $1$ as a fraction with a common denominator.

$\frac{2 x}{9} = \frac{3}{3} + \frac{1}{3}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{2 x}{9} = \frac{3 + 1}{3}$

Step 2.4

Add $3$ and $1$ .

$\frac{2 x}{9} = \frac{4}{3}$

Step 3

Multiply both sides of the equation by $\frac{9}{2}$ .

$\frac{9}{2} \cdot \frac{2 x}{9} = \frac{9}{2} \cdot \frac{4}{3}$

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 $\frac{9}{2} \cdot \frac{2 x}{9}$ .

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Step 4.1.1.1

Cancel the common factor of $9$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{9}{2} \cdot \frac{2 x}{9} = \frac{9}{2} \cdot \frac{4}{3}$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{9}{2} \cdot \frac{4}{3}$

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 $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{9}{2} \cdot \frac{4}{3}$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{9}{2} \cdot \frac{4}{3}$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{9}{2} \cdot \frac{4}{3}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{9}{2} \cdot \frac{4}{3}$ .

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Step 4.2.1.1

Cancel the common factor of $3$ .

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Step 4.2.1.1.1

Factor $3$ out of $9$ .

$x = \frac{3 (3)}{2} \cdot \frac{4}{3}$

Step 4.2.1.1.2

Cancel the common factor.

$x = \frac{3 \cdot 3}{2} \cdot \frac{4}{3}$

Step 4.2.1.1.3

Rewrite the expression.

$x = \frac{3}{2} \cdot 4$

Step 4.2.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.2.1

Factor $2$ out of $4$ .

$x = \frac{3}{2} \cdot (2 (2))$

Step 4.2.1.2.2

Cancel the common factor.

$x = \frac{3}{2} \cdot (2 \cdot 2)$

Step 4.2.1.2.3

Rewrite the expression.

$x = 3 \cdot 2$

Step 4.2.1.3

Multiply $3$ by $2$ .

$x = 6$