Pre-Algebra Examples

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

Step 1

Remove parentheses.

$\frac{1}{3} x - 3 - \frac{3}{4} x - 5$

Step 2

Simplify each term.

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Step 2.1

Combine $\frac{1}{3}$ and $x$ .

$\frac{x}{3} - 3 - \frac{3}{4} x - 5$

Step 2.2

Combine $x$ and $\frac{3}{4}$ .

$\frac{x}{3} - 3 - \frac{x \cdot 3}{4} - 5$

Step 2.3

Move $3$ to the left of $x$ .

$\frac{x}{3} - 3 - \frac{3 x}{4} - 5$

Step 3

To write $\frac{x}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x}{3} \cdot \frac{4}{4} - \frac{3 x}{4} - 3 - 5$

Step 4

To write $- \frac{3 x}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x}{3} \cdot \frac{4}{4} - \frac{3 x}{4} \cdot \frac{3}{3} - 3 - 5$

Step 5

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.1

Multiply $\frac{x}{3}$ by $\frac{4}{4}$ .

$\frac{x \cdot 4}{3 \cdot 4} - \frac{3 x}{4} \cdot \frac{3}{3} - 3 - 5$

Step 5.2

Multiply $3$ by $4$ .

$\frac{x \cdot 4}{12} - \frac{3 x}{4} \cdot \frac{3}{3} - 3 - 5$

Step 5.3

Multiply $\frac{3 x}{4}$ by $\frac{3}{3}$ .

$\frac{x \cdot 4}{12} - \frac{3 x \cdot 3}{4 \cdot 3} - 3 - 5$

Step 5.4

Multiply $4$ by $3$ .

$\frac{x \cdot 4}{12} - \frac{3 x \cdot 3}{12} - 3 - 5$

Step 6

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - 3 x \cdot 3}{12} - 3 - 5$

Step 7

Find the common denominator.

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Step 7.1

Write $- 3$ as a fraction with denominator $1$ .

$\frac{x \cdot 4 - 3 x \cdot 3}{12} + \frac{- 3}{1} - 5$

Step 7.2

Multiply $\frac{- 3}{1}$ by $\frac{12}{12}$ .

$\frac{x \cdot 4 - 3 x \cdot 3}{12} + \frac{- 3}{1} \cdot \frac{12}{12} - 5$

Step 7.3

Multiply $\frac{- 3}{1}$ by $\frac{12}{12}$ .

$\frac{x \cdot 4 - 3 x \cdot 3}{12} + \frac{- 3 \cdot 12}{12} - 5$

Step 7.4

Write $- 5$ as a fraction with denominator $1$ .

$\frac{x \cdot 4 - 3 x \cdot 3}{12} + \frac{- 3 \cdot 12}{12} + \frac{- 5}{1}$

Step 7.5

Multiply $\frac{- 5}{1}$ by $\frac{12}{12}$ .

$\frac{x \cdot 4 - 3 x \cdot 3}{12} + \frac{- 3 \cdot 12}{12} + \frac{- 5}{1} \cdot \frac{12}{12}$

Step 7.6

Multiply $\frac{- 5}{1}$ by $\frac{12}{12}$ .

$\frac{x \cdot 4 - 3 x \cdot 3}{12} + \frac{- 3 \cdot 12}{12} + \frac{- 5 \cdot 12}{12}$

Step 8

Combine the numerators over the common denominator.

$\frac{x \cdot 4 - 3 x \cdot 3 - 3 \cdot 12 - 5 \cdot 12}{12}$

Step 9

Simplify each term.

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Step 9.1

Move $4$ to the left of $x$ .

$\frac{4 \cdot x - 3 x \cdot 3 - 3 \cdot 12 - 5 \cdot 12}{12}$

Step 9.2

Multiply $3$ by $- 3$ .

$\frac{4 x - 9 x - 3 \cdot 12 - 5 \cdot 12}{12}$

Step 9.3

Multiply $- 3$ by $12$ .

$\frac{4 x - 9 x - 36 - 5 \cdot 12}{12}$

Step 9.4

Multiply $- 5$ by $12$ .

$\frac{4 x - 9 x - 36 - 60}{12}$

Step 10

Simplify terms.

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Step 10.1

Subtract $9 x$ from $4 x$ .

$\frac{- 5 x - 36 - 60}{12}$

Step 10.2

Subtract $60$ from $- 36$ .

$\frac{- 5 x - 96}{12}$

Step 10.3

Factor $- 1$ out of $- 5 x$ .

$\frac{- (5 x) - 96}{12}$

Step 10.4

Rewrite $- 96$ as $- 1 (96)$ .

$\frac{- (5 x) - 1 (96)}{12}$

Step 10.5

Factor $- 1$ out of $- (5 x) - 1 (96)$ .

$\frac{- (5 x + 96)}{12}$

Step 10.6

Simplify the expression.

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Step 10.6.1

Rewrite $- (5 x + 96)$ as $- 1 (5 x + 96)$ .

$\frac{- 1 (5 x + 96)}{12}$

Step 10.6.2

Move the negative in front of the fraction.

$- \frac{5 x + 96}{12}$