Algebra Examples

$\frac{1}{4} + \frac{1}{5} = \frac{x - 3}{20}$

Step 1

Rewrite the equation as $\frac{x - 3}{20} = \frac{1}{4} + \frac{1}{5}$ .

$\frac{x - 3}{20} = \frac{1}{4} + \frac{1}{5}$

Step 2

Multiply both sides of the equation by $20$ .

$20 \frac{x - 3}{20} = 20 (\frac{1}{4} + \frac{1}{5})$

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 $20$ .

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Step 3.1.1.1

Cancel the common factor.

$20 \frac{x - 3}{20} = 20 (\frac{1}{4} + \frac{1}{5})$

Step 3.1.1.2

Rewrite the expression.

$x - 3 = 20 (\frac{1}{4} + \frac{1}{5})$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $20 (\frac{1}{4} + \frac{1}{5})$ .

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Step 3.2.1.1

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x - 3 = 20 (\frac{1}{4} \cdot \frac{5}{5} + \frac{1}{5})$

Step 3.2.1.2

To write $\frac{1}{5}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$x - 3 = 20 (\frac{1}{4} \cdot \frac{5}{5} + \frac{1}{5} \cdot \frac{4}{4})$

Step 3.2.1.3

Write each expression with a common denominator of $20$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.2.1.3.1

Multiply $\frac{1}{4}$ by $\frac{5}{5}$ .

$x - 3 = 20 (\frac{5}{4 \cdot 5} + \frac{1}{5} \cdot \frac{4}{4})$

Step 3.2.1.3.2

Multiply $4$ by $5$ .

$x - 3 = 20 (\frac{5}{20} + \frac{1}{5} \cdot \frac{4}{4})$

Step 3.2.1.3.3

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$x - 3 = 20 (\frac{5}{20} + \frac{4}{5 \cdot 4})$

Step 3.2.1.3.4

Multiply $5$ by $4$ .

$x - 3 = 20 (\frac{5}{20} + \frac{4}{20})$

Step 3.2.1.4

Simplify the expression.

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Step 3.2.1.4.1

Combine the numerators over the common denominator.

$x - 3 = 20 \frac{5 + 4}{20}$

Step 3.2.1.4.2

Add $5$ and $4$ .

$x - 3 = 20 (\frac{9}{20})$

Step 3.2.1.5

Cancel the common factor of $20$ .

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Step 3.2.1.5.1

Cancel the common factor.

$x - 3 = 20 (\frac{9}{20})$

Step 3.2.1.5.2

Rewrite the expression.

$x - 3 = 9$

Step 4

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

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Step 4.1

Add $3$ to both sides of the equation.

$x = 9 + 3$

Step 4.2

Add $9$ and $3$ .

$x = 12$