Algebra Examples

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

Step 1

Simplify $\frac{3 x}{2} + x$ .

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Step 1.1

To write $x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.2

Simplify terms.

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Step 1.2.1

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

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.3

Simplify the numerator.

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Step 1.3.1

Move $2$ to the left of $x$ .

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

Step 1.3.2

Add $3 x$ and $2 x$ .

$\frac{5 x}{2} = \frac{1}{3}$

Step 2

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} \cdot \frac{1}{3}$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{2}{5} \cdot \frac{5 x}{2}$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} \cdot \frac{1}{3}$

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{2}{5} \cdot \frac{1}{3}$

Step 3.1.1.2

Cancel the common factor of $5$ .

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Step 3.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{2}{5} \cdot \frac{1}{3}$

Step 3.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{2}{5} \cdot \frac{1}{3}$

Step 3.1.1.2.3

Rewrite the expression.

$x = \frac{2}{5} \cdot \frac{1}{3}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $\frac{2}{5} \cdot \frac{1}{3}$ .

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Step 3.2.1.1

Multiply $\frac{2}{5}$ by $\frac{1}{3}$ .

$x = \frac{2}{5 \cdot 3}$

Step 3.2.1.2

Multiply $5$ by $3$ .

$x = \frac{2}{15}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{2}{15}$

Decimal Form:

$x = 0.1\overline{3}$