Pre-Algebra Examples

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

Step 1

Combine $\frac{5}{2}$ and $x$ .

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

Step 2

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

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Step 2.1

Add $\frac{1}{3}$ to both sides of the equation.

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

Step 2.2

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 2.3

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 2.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

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

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

Step 2.4.2

Multiply $2$ by $3$ .

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

Step 2.4.3

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

$\frac{5 x}{2} = - \frac{3}{6} + \frac{2}{3 \cdot 2}$

Step 2.4.4

Multiply $3$ by $2$ .

$\frac{5 x}{2} = - \frac{3}{6} + \frac{2}{6}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{5 x}{2} = \frac{- 3 + 2}{6}$

Step 2.6

Add $- 3$ and $2$ .

$\frac{5 x}{2} = \frac{- 1}{6}$

Step 2.7

Move the negative in front of the fraction.

$\frac{5 x}{2} = - \frac{1}{6}$

Step 3

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

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} (- \frac{1}{6})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} (- \frac{1}{6})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{2}{5} (- \frac{1}{6})$

Step 4.1.1.2

Cancel the common factor of $5$ .

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Step 4.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{2}{5} (- \frac{1}{6})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{2}{5} (- \frac{1}{6})$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{2}{5} (- \frac{1}{6})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{5} (- \frac{1}{6})$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$x = \frac{2}{5} \cdot \frac{- 1}{6}$

Step 4.2.1.1.2

Factor $2$ out of $6$ .

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

Step 4.2.1.1.3

Cancel the common factor.

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

Step 4.2.1.1.4

Rewrite the expression.

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

Step 4.2.1.2

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

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

Step 4.2.1.3

Simplify the expression.

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Step 4.2.1.3.1

Multiply $5$ by $3$ .

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

Step 4.2.1.3.2

Move the negative in front of the fraction.

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.0\overline{6}$