Pre-Algebra Examples

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

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

Step 1

Remove parentheses.

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

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

Step 2

Simplify each term.

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Step 2.1

Combine

\frac{1}{3}

$\frac{1}{3}$ and

x

$x$ .

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

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

Step 2.2

Combine

x

$x$ and

\frac{3}{4}

$\frac{3}{4}$ .

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

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

Step 2.3

Move

3

$3$ to the left of

x

$x$ .

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

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

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

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

Step 3

To write

\frac{x}{3}

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

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 4

To write

- \frac{3 x}{4}

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 5

Write each expression with a common denominator of

12

$12$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 5.1

Multiply

\frac{x}{3}

$\frac{x}{3}$ by

\frac{4}{4}

$\frac{4}{4}$ .

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

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

Step 5.2

Multiply

3

$3$ by

4

$4$ .

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

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

Step 5.3

Multiply

\frac{3 x}{4}

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

\frac{3}{3}

$\frac{3}{3}$ .

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

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

Step 5.4

Multiply

4

$4$ by

3

$3$ .

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

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

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

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

Step 6

Combine the numerators over the common denominator.

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

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

Step 7

Find the common denominator.

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Step 7.1

Write

- 3

$- 3$ as a fraction with denominator

1

$1$ .

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

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

Step 7.2

Multiply

\frac{- 3}{1}

$\frac{- 3}{1}$ by

\frac{12}{12}

$\frac{12}{12}$ .

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

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

Step 7.3

Multiply

\frac{- 3}{1}

$\frac{- 3}{1}$ by

\frac{12}{12}

$\frac{12}{12}$ .

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

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

Step 7.4

Write

- 5

$- 5$ as a fraction with denominator

1

$1$ .

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

$\frac{- 5}{1}$ by

\frac{12}{12}

$\frac{12}{12}$ .

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

$\frac{- 5}{1}$ by

\frac{12}{12}

$\frac{12}{12}$ .

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

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

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

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

Step 9

Simplify each term.

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Step 9.1

Move

4

$4$ to the left of

x

$x$ .

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

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

Step 9.2

Multiply

3

$3$ by

- 3

$- 3$ .

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

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

Step 9.3

Multiply

- 3

$- 3$ by

12

$12$ .

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

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

Step 9.4

Multiply

- 5

$- 5$ by

12

$12$ .

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

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

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

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

Step 10

Simplify terms.

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Step 10.1

Subtract

9 x

$9 x$ from

4 x

$4 x$ .

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

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

Step 10.2

Subtract

60

$60$ from

- 36

$- 36$ .

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

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

Step 10.3

Factor

- 1

$- 1$ out of

- 5 x

$- 5 x$ .

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

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

Step 10.4

Rewrite

- 96

$- 96$ as

- 1 (96)

$- 1 (96)$ .

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

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

Step 10.5

Factor

- 1

$- 1$ out of

- (5 x) - 1 (96)

$- (5 x) - 1 (96)$ .

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

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

Step 10.6

Simplify the expression.

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Step 10.6.1

Rewrite

- (5 x + 96)

$- (5 x + 96)$ as

- 1 (5 x + 96)

$- 1 (5 x + 96)$ .

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

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

Step 10.6.2

Move the negative in front of the fraction.

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

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

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

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

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

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