Finite Math Examples

$\frac{1}{2} x + \frac{1}{6} = \frac{7}{20}$

Step 1

Combine $\frac{1}{2}$ and $x$ .

$\frac{x}{2} + \frac{1}{6} = \frac{7}{20}$

Step 2

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

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Step 2.1

Subtract $\frac{1}{6}$ from both sides of the equation.

$\frac{x}{2} = \frac{7}{20} - \frac{1}{6}$

Step 2.2

To write $\frac{7}{20}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{2} = \frac{7}{20} \cdot \frac{3}{3} - \frac{1}{6}$

Step 2.3

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{x}{2} = \frac{7}{20} \cdot \frac{3}{3} - \frac{1}{6} \cdot \frac{10}{10}$

Step 2.4

Write each expression with a common denominator of $60$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{7}{20}$ by $\frac{3}{3}$ .

$\frac{x}{2} = \frac{7 \cdot 3}{20 \cdot 3} - \frac{1}{6} \cdot \frac{10}{10}$

Step 2.4.2

Multiply $20$ by $3$ .

$\frac{x}{2} = \frac{7 \cdot 3}{60} - \frac{1}{6} \cdot \frac{10}{10}$

Step 2.4.3

Multiply $\frac{1}{6}$ by $\frac{10}{10}$ .

$\frac{x}{2} = \frac{7 \cdot 3}{60} - \frac{10}{6 \cdot 10}$

Step 2.4.4

Multiply $6$ by $10$ .

$\frac{x}{2} = \frac{7 \cdot 3}{60} - \frac{10}{60}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{x}{2} = \frac{7 \cdot 3 - 10}{60}$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Multiply $7$ by $3$ .

$\frac{x}{2} = \frac{21 - 10}{60}$

Step 2.6.2

Subtract $10$ from $21$ .

$\frac{x}{2} = \frac{11}{60}$

Step 3

Multiply both sides of the equation by $2$ .

$2 \frac{x}{2} = 2 (\frac{11}{60})$

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

Cancel the common factor of $2$ .

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Step 4.1.1.1

Cancel the common factor.

$2 \frac{x}{2} = 2 (\frac{11}{60})$

Step 4.1.1.2

Rewrite the expression.

$x = 2 (\frac{11}{60})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Factor $2$ out of $60$ .

$x = 2 \frac{11}{2 (30)}$

Step 4.2.1.2

Cancel the common factor.

$x = 2 \frac{11}{2 \cdot 30}$

Step 4.2.1.3

Rewrite the expression.

$x = \frac{11}{30}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{30}$

Decimal Form:

$x = 0.3\overline{6}$