Finite Math Examples

$20 (\frac{x - 5}{11} - \frac{x - 11}{5})$

Step 1

To write $\frac{x - 5}{11}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$20 (\frac{x - 5}{11} \cdot \frac{5}{5} - \frac{x - 11}{5})$

Step 2

To write $- \frac{x - 11}{5}$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$20 (\frac{x - 5}{11} \cdot \frac{5}{5} - \frac{x - 11}{5} \cdot \frac{11}{11})$

Step 3

Write each expression with a common denominator of $55$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{x - 5}{11}$ by $\frac{5}{5}$ .

$20 (\frac{(x - 5) \cdot 5}{11 \cdot 5} - \frac{x - 11}{5} \cdot \frac{11}{11})$

Step 3.2

Multiply $11$ by $5$ .

$20 (\frac{(x - 5) \cdot 5}{55} - \frac{x - 11}{5} \cdot \frac{11}{11})$

Step 3.3

Multiply $\frac{x - 11}{5}$ by $\frac{11}{11}$ .

$20 (\frac{(x - 5) \cdot 5}{55} - \frac{(x - 11) \cdot 11}{5 \cdot 11})$

Step 3.4

Multiply $5$ by $11$ .

$20 (\frac{(x - 5) \cdot 5}{55} - \frac{(x - 11) \cdot 11}{55})$

Step 4

Combine the numerators over the common denominator.

$20 \frac{(x - 5) \cdot 5 - (x - 11) \cdot 11}{55}$

Step 5

Simplify the numerator.

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Step 5.1

Apply the distributive property.

$20 \frac{x \cdot 5 - 5 \cdot 5 - (x - 11) \cdot 11}{55}$

Step 5.2

Move $5$ to the left of $x$ .

$20 \frac{5 \cdot x - 5 \cdot 5 - (x - 11) \cdot 11}{55}$

Step 5.3

Multiply $- 5$ by $5$ .

$20 \frac{5 \cdot x - 25 - (x - 11) \cdot 11}{55}$

Step 5.4

Apply the distributive property.

$20 \frac{5 x - 25 + (- x - - 11) \cdot 11}{55}$

Step 5.5

Multiply $- 1$ by $- 11$ .

$20 \frac{5 x - 25 + (- x + 11) \cdot 11}{55}$

Step 5.6

Apply the distributive property.

$20 \frac{5 x - 25 - x \cdot 11 + 11 \cdot 11}{55}$

Step 5.7

Multiply $11$ by $- 1$ .

$20 \frac{5 x - 25 - 11 x + 11 \cdot 11}{55}$

Step 5.8

Multiply $11$ by $11$ .

$20 \frac{5 x - 25 - 11 x + 121}{55}$

Step 5.9

Subtract $11 x$ from $5 x$ .

$20 \frac{- 6 x - 25 + 121}{55}$

Step 5.10

Add $- 25$ and $121$ .

$20 \frac{- 6 x + 96}{55}$

Step 5.11

Factor $6$ out of $- 6 x + 96$ .

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Step 5.11.1

Factor $6$ out of $- 6 x$ .

$20 \frac{6 (- x) + 96}{55}$

Step 5.11.2

Factor $6$ out of $96$ .

$20 \frac{6 (- x) + 6 (16)}{55}$

Step 5.11.3

Factor $6$ out of $6 (- x) + 6 (16)$ .

$20 \frac{6 (- x + 16)}{55}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $5$ .

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Step 6.1.1

Factor $5$ out of $20$ .

$5 (4) \frac{6 (- x + 16)}{55}$

Step 6.1.2

Factor $5$ out of $55$ .

$5 \cdot 4 \frac{6 (- x + 16)}{5 \cdot 11}$

Step 6.1.3

Cancel the common factor.

$5 \cdot 4 \frac{6 (- x + 16)}{5 \cdot 11}$

Step 6.1.4

Rewrite the expression.

$4 \frac{6 (- x + 16)}{11}$

Step 6.2

Combine $4$ and $\frac{6 (- x + 16)}{11}$ .

$\frac{4 (6 (- x + 16))}{11}$

Step 6.3

Multiply $6$ by $4$ .

$\frac{24 (- x + 16)}{11}$

Step 6.4

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

$\frac{24 (- (x) + 16)}{11}$

Step 6.5

Rewrite $16$ as $- 1 (- 16)$ .

$\frac{24 (- (x) - 1 (- 16))}{11}$

Step 6.6

Factor $- 1$ out of $- (x) - 1 (- 16)$ .

$\frac{24 (- (x - 16))}{11}$

Step 6.7

Simplify the expression.

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Step 6.7.1

Rewrite $- (x - 16)$ as $- 1 (x - 16)$ .

$\frac{24 (- 1 (x - 16))}{11}$

Step 6.7.2

Move the negative in front of the fraction.

$- \frac{24 (x - 16)}{11}$