Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Add $2$ to both sides of the equation.

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

Step 1.2

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

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

Step 1.3

Combine $2$ and $\frac{3}{3}$ .

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

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $2$ by $3$ .

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

Step 1.5.2

Add $1$ and $6$ .

$\frac{x}{5} = \frac{7}{3}$

Step 2

Multiply both sides of the equation by $5$ .

$5 \frac{x}{5} = 5 (\frac{7}{3})$

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

Cancel the common factor of $5$ .

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Step 3.1.1.1

Cancel the common factor.

$5 \frac{x}{5} = 5 (\frac{7}{3})$

Step 3.1.1.2

Rewrite the expression.

$x = 5 (\frac{7}{3})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $5 (\frac{7}{3})$ .

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Step 3.2.1.1

Combine $5$ and $\frac{7}{3}$ .

$x = \frac{5 \cdot 7}{3}$

Step 3.2.1.2

Multiply $5$ by $7$ .

$x = \frac{35}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{35}{3}$

Decimal Form:

$x = 11.\overline{6}$

Mixed Number Form:

$x = 11 \frac{2}{3}$