Pre-Algebra Examples

$4 x - \frac{1}{5} = \frac{1}{15}$

Step 1

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

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Step 1.1

Add $\frac{1}{5}$ to both sides of the equation.

$4 x = \frac{1}{15} + \frac{1}{5}$

Step 1.2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$4 x = \frac{1}{15} + \frac{1}{5} \cdot \frac{3}{3}$

Step 1.3

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

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Step 1.3.1

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

$4 x = \frac{1}{15} + \frac{3}{5 \cdot 3}$

Step 1.3.2

Multiply $5$ by $3$ .

$4 x = \frac{1}{15} + \frac{3}{15}$

Step 1.4

Combine the numerators over the common denominator.

$4 x = \frac{1 + 3}{15}$

Step 1.5

Add $1$ and $3$ .

$4 x = \frac{4}{15}$

Step 2

Divide each term in $4 x = \frac{4}{15}$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 x = \frac{4}{15}$ by $4$ .

$\frac{4 x}{4} = \frac{\frac{4}{15}}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{\frac{4}{15}}{4}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{4}{15}}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{4}{15} \cdot \frac{1}{4}$

Step 2.3.2

Cancel the common factor of $4$ .

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Step 2.3.2.1

Cancel the common factor.

$x = \frac{4}{15} \cdot \frac{1}{4}$

Step 2.3.2.2

Rewrite the expression.

$x = \frac{1}{15}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{15}$

Decimal Form:

$x = 0.0\overline{6}$