Pre-Algebra Examples

$\frac{x}{5} - \frac{x}{4} = 2$

Step 1

Simplify $\frac{x}{5} - \frac{x}{4}$ .

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Step 1.1

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

$\frac{x}{5} \cdot \frac{4}{4} - \frac{x}{4} = 2$

Step 1.2

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

$\frac{x}{5} \cdot \frac{4}{4} - \frac{x}{4} \cdot \frac{5}{5} = 2$

Step 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 1.3.1

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

$\frac{x \cdot 4}{5 \cdot 4} - \frac{x}{4} \cdot \frac{5}{5} = 2$

Step 1.3.2

Multiply $5$ by $4$ .

$\frac{x \cdot 4}{20} - \frac{x}{4} \cdot \frac{5}{5} = 2$

Step 1.3.3

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

$\frac{x \cdot 4}{20} - \frac{x \cdot 5}{4 \cdot 5} = 2$

Step 1.3.4

Multiply $4$ by $5$ .

$\frac{x \cdot 4}{20} - \frac{x \cdot 5}{20} = 2$

Step 1.4

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - x \cdot 5}{20} = 2$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $x$ out of $x \cdot 4 - x \cdot 5$ .

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Step 1.5.1.1

Factor $x$ out of $x \cdot 4$ .

$\frac{x (4) - x \cdot 5}{20} = 2$

Step 1.5.1.2

Factor $x$ out of $- x \cdot 5$ .

$\frac{x (4) + x (- 1 \cdot 5)}{20} = 2$

Step 1.5.1.3

Factor $x$ out of $x (4) + x (- 1 \cdot 5)$ .

$\frac{x (4 - 1 \cdot 5)}{20} = 2$

Step 1.5.2

Multiply $- 1$ by $5$ .

$\frac{x (4 - 5)}{20} = 2$

Step 1.5.3

Subtract $5$ from $4$ .

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

Step 1.6

Simplify the expression.

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Step 1.6.1

Move $- 1$ to the left of $x$ .

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

Step 1.6.2

Move the negative in front of the fraction.

$- \frac{x}{20} = 2$

Step 2

Multiply both sides of the equation by $- 20$ .

$- 20 (- \frac{x}{20}) = - 20 \cdot 2$

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

Simplify $- 20 (- \frac{x}{20})$ .

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Step 3.1.1.1

Cancel the common factor of $20$ .

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Step 3.1.1.1.1

Move the leading negative in $- \frac{x}{20}$ into the numerator.

$- 20 \frac{- x}{20} = - 20 \cdot 2$

Step 3.1.1.1.2

Factor $20$ out of $- 20$ .

$20 (- 1) \frac{- x}{20} = - 20 \cdot 2$

Step 3.1.1.1.3

Cancel the common factor.

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

Step 3.1.1.1.4

Rewrite the expression.

$- - x = - 20 \cdot 2$

Step 3.1.1.2

Multiply.

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Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 20 \cdot 2$

Step 3.1.1.2.2

Multiply $x$ by $1$ .

$x = - 20 \cdot 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $- 20$ by $2$ .

$x = - 40$