Pre-Algebra Examples

$\frac{- 9 x - 4 x}{7} - \frac{- 2 x + 9}{4}$

Step 1

Subtract $4 x$ from $- 9 x$ .

$\frac{- 13 x}{7} - \frac{- 2 x + 9}{4}$

Step 2

Move the negative in front of the fraction.

$- \frac{13 x}{7} - \frac{- 2 x + 9}{4}$

Step 3

To write $- \frac{13 x}{7}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{13 x}{7} \cdot \frac{4}{4} - \frac{- 2 x + 9}{4}$

Step 4

To write $- \frac{- 2 x + 9}{4}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{13 x}{7} \cdot \frac{4}{4} - \frac{- 2 x + 9}{4} \cdot \frac{7}{7}$

Step 5

Write each expression with a common denominator of $28$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{13 x}{7}$ by $\frac{4}{4}$ .

$- \frac{13 x \cdot 4}{7 \cdot 4} - \frac{- 2 x + 9}{4} \cdot \frac{7}{7}$

Step 5.2

Multiply $7$ by $4$ .

$- \frac{13 x \cdot 4}{28} - \frac{- 2 x + 9}{4} \cdot \frac{7}{7}$

Step 5.3

Multiply $\frac{- 2 x + 9}{4}$ by $\frac{7}{7}$ .

$- \frac{13 x \cdot 4}{28} - \frac{(- 2 x + 9) \cdot 7}{4 \cdot 7}$

Step 5.4

Multiply $4$ by $7$ .

$- \frac{13 x \cdot 4}{28} - \frac{(- 2 x + 9) \cdot 7}{28}$

Step 6

Combine the numerators over the common denominator.

$\frac{- 13 x \cdot 4 - (- 2 x + 9) \cdot 7}{28}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $4$ by $- 13$ .

$\frac{- 52 x - (- 2 x + 9) \cdot 7}{28}$

Step 7.2

Apply the distributive property.

$\frac{- 52 x + (- (- 2 x) - 1 \cdot 9) \cdot 7}{28}$

Step 7.3

Multiply $- 2$ by $- 1$ .

$\frac{- 52 x + (2 x - 1 \cdot 9) \cdot 7}{28}$

Step 7.4

Multiply $- 1$ by $9$ .

$\frac{- 52 x + (2 x - 9) \cdot 7}{28}$

Step 7.5

Apply the distributive property.

$\frac{- 52 x + 2 x \cdot 7 - 9 \cdot 7}{28}$

Step 7.6

Multiply $7$ by $2$ .

$\frac{- 52 x + 14 x - 9 \cdot 7}{28}$

Step 7.7

Multiply $- 9$ by $7$ .

$\frac{- 52 x + 14 x - 63}{28}$

Step 7.8

Add $- 52 x$ and $14 x$ .

$\frac{- 38 x - 63}{28}$

Step 8

Simplify with factoring out.

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Step 8.1

Factor $- 1$ out of $- 38 x$ .

$\frac{- (38 x) - 63}{28}$

Step 8.2

Rewrite $- 63$ as $- 1 (63)$ .

$\frac{- (38 x) - 1 (63)}{28}$

Step 8.3

Factor $- 1$ out of $- (38 x) - 1 (63)$ .

$\frac{- (38 x + 63)}{28}$

Step 8.4

Simplify the expression.

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Step 8.4.1

Rewrite $- (38 x + 63)$ as $- 1 (38 x + 63)$ .

$\frac{- 1 (38 x + 63)}{28}$

Step 8.4.2

Move the negative in front of the fraction.

$- \frac{38 x + 63}{28}$