Pre-Algebra Examples

$\frac{1}{x} = \frac{1}{6} + \frac{1}{10} + \frac{1}{15}$

Step 1

Simplify $\frac{1}{6} + \frac{1}{10} + \frac{1}{15}$ .

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Step 1.1

Find the common denominator.

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Step 1.1.1

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{1}{x} = \frac{1}{6} \cdot \frac{5}{5} + \frac{1}{10} + \frac{1}{15}$

Step 1.1.2

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{1}{x} = \frac{5}{6 \cdot 5} + \frac{1}{10} + \frac{1}{15}$

Step 1.1.3

Multiply $\frac{1}{10}$ by $\frac{3}{3}$ .

$\frac{1}{x} = \frac{5}{6 \cdot 5} + \frac{1}{10} \cdot \frac{3}{3} + \frac{1}{15}$

Step 1.1.4

Multiply $\frac{1}{10}$ by $\frac{3}{3}$ .

$\frac{1}{x} = \frac{5}{6 \cdot 5} + \frac{3}{10 \cdot 3} + \frac{1}{15}$

Step 1.1.5

Multiply $\frac{1}{15}$ by $\frac{2}{2}$ .

$\frac{1}{x} = \frac{5}{6 \cdot 5} + \frac{3}{10 \cdot 3} + \frac{1}{15} \cdot \frac{2}{2}$

Step 1.1.6

Multiply $\frac{1}{15}$ by $\frac{2}{2}$ .

$\frac{1}{x} = \frac{5}{6 \cdot 5} + \frac{3}{10 \cdot 3} + \frac{2}{15 \cdot 2}$

Step 1.1.7

Reorder the factors of $6 \cdot 5$ .

$\frac{1}{x} = \frac{5}{5 \cdot 6} + \frac{3}{10 \cdot 3} + \frac{2}{15 \cdot 2}$

Step 1.1.8

Multiply $5$ by $6$ .

$\frac{1}{x} = \frac{5}{30} + \frac{3}{10 \cdot 3} + \frac{2}{15 \cdot 2}$

Step 1.1.9

Reorder the factors of $10 \cdot 3$ .

$\frac{1}{x} = \frac{5}{30} + \frac{3}{3 \cdot 10} + \frac{2}{15 \cdot 2}$

Step 1.1.10

Multiply $3$ by $10$ .

$\frac{1}{x} = \frac{5}{30} + \frac{3}{30} + \frac{2}{15 \cdot 2}$

Step 1.1.11

Reorder the factors of $15 \cdot 2$ .

$\frac{1}{x} = \frac{5}{30} + \frac{3}{30} + \frac{2}{2 \cdot 15}$

Step 1.1.12

Multiply $2$ by $15$ .

$\frac{1}{x} = \frac{5}{30} + \frac{3}{30} + \frac{2}{30}$

Step 1.2

Combine the numerators over the common denominator.

$\frac{1}{x} = \frac{5 + 3 + 2}{30}$

Step 1.3

Simplify by adding numbers.

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Step 1.3.1

Add $5$ and $3$ .

$\frac{1}{x} = \frac{8 + 2}{30}$

Step 1.3.2

Add $8$ and $2$ .

$\frac{1}{x} = \frac{10}{30}$

Step 1.4

Cancel the common factor of $10$ and $30$ .

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Step 1.4.1

Factor $10$ out of $10$ .

$\frac{1}{x} = \frac{10 (1)}{30}$

Step 1.4.2

Cancel the common factors.

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Step 1.4.2.1

Factor $10$ out of $30$ .

$\frac{1}{x} = \frac{10 \cdot 1}{10 \cdot 3}$

Step 1.4.2.2

Cancel the common factor.

$\frac{1}{x} = \frac{10 \cdot 1}{10 \cdot 3}$

Step 1.4.2.3

Rewrite the expression.

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

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 3$

Step 3