Pre-Algebra Examples

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

Step 1

Combine $\frac{1}{3}$ and $x$ .

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

Step 2

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

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Step 2.1

Subtract $\frac{2}{5}$ from both sides of the equation.

$\frac{x}{3} = \frac{1}{15} - \frac{2}{5}$

Step 2.2

To write $- \frac{2}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.3

Write each expression with a common denominator of $15$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

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

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

Step 2.3.2

Multiply $5$ by $3$ .

$\frac{x}{3} = \frac{1}{15} - \frac{2 \cdot 3}{15}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{x}{3} = \frac{1 - 2 \cdot 3}{15}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 2$ by $3$ .

$\frac{x}{3} = \frac{1 - 6}{15}$

Step 2.5.2

Subtract $6$ from $1$ .

$\frac{x}{3} = \frac{- 5}{15}$

Step 2.6

Cancel the common factor of $- 5$ and $15$ .

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Step 2.6.1

Factor $5$ out of $- 5$ .

$\frac{x}{3} = \frac{5 (- 1)}{15}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $5$ out of $15$ .

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

Step 2.6.2.2

Cancel the common factor.

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

Step 2.6.2.3

Rewrite the expression.

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

Step 2.7

Move the negative in front of the fraction.

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

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$x = - 1$