Algebra Examples

$(\frac{1}{10} x - \frac{2}{3}) - (\frac{4}{5} x - \frac{1}{6})$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{1}{10}$ and $x$ .

$\frac{x}{10} - \frac{2}{3} - (\frac{4}{5} x - \frac{1}{6})$

Step 1.2

Combine $\frac{4}{5}$ and $x$ .

$\frac{x}{10} - \frac{2}{3} - (\frac{4 x}{5} - \frac{1}{6})$

Step 1.3

Apply the distributive property.

$\frac{x}{10} - \frac{2}{3} - \frac{4 x}{5} - - \frac{1}{6}$

Step 1.4

Multiply $- - \frac{1}{6}$ .

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Step 1.4.1

Multiply $- 1$ by $- 1$ .

$\frac{x}{10} - \frac{2}{3} - \frac{4 x}{5} + 1 (\frac{1}{6})$

Step 1.4.2

Multiply $\frac{1}{6}$ by $1$ .

$\frac{x}{10} - \frac{2}{3} - \frac{4 x}{5} + \frac{1}{6}$

Step 2

To write $- \frac{4 x}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{10} - \frac{4 x}{5} \cdot \frac{2}{2} - \frac{2}{3} + \frac{1}{6}$

Step 3

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

Multiply $\frac{4 x}{5}$ by $\frac{2}{2}$ .

$\frac{x}{10} - \frac{4 x \cdot 2}{5 \cdot 2} - \frac{2}{3} + \frac{1}{6}$

Step 3.2

Multiply $5$ by $2$ .

$\frac{x}{10} - \frac{4 x \cdot 2}{10} - \frac{2}{3} + \frac{1}{6}$

Step 4

Combine the numerators over the common denominator.

$\frac{x - 4 x \cdot 2}{10} - \frac{2}{3} + \frac{1}{6}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{x - 4 x \cdot 2}{10}$ by $\frac{3}{3}$ .

$\frac{x - 4 x \cdot 2}{10} \cdot \frac{3}{3} - \frac{2}{3} + \frac{1}{6}$

Step 5.2

Multiply $\frac{x - 4 x \cdot 2}{10}$ by $\frac{3}{3}$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{10 \cdot 3} - \frac{2}{3} + \frac{1}{6}$

Step 5.3

Multiply $\frac{2}{3}$ by $\frac{10}{10}$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{10 \cdot 3} - (\frac{2}{3} \cdot \frac{10}{10}) + \frac{1}{6}$

Step 5.4

Multiply $\frac{2}{3}$ by $\frac{10}{10}$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{10 \cdot 3} - \frac{2 \cdot 10}{3 \cdot 10} + \frac{1}{6}$

Step 5.5

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{10 \cdot 3} - \frac{2 \cdot 10}{3 \cdot 10} + \frac{1}{6} \cdot \frac{5}{5}$

Step 5.6

Multiply $\frac{1}{6}$ by $\frac{5}{5}$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{10 \cdot 3} - \frac{2 \cdot 10}{3 \cdot 10} + \frac{5}{6 \cdot 5}$

Step 5.7

Reorder the factors of $10 \cdot 3$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{3 \cdot 10} - \frac{2 \cdot 10}{3 \cdot 10} + \frac{5}{6 \cdot 5}$

Step 5.8

Multiply $3$ by $10$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{30} - \frac{2 \cdot 10}{3 \cdot 10} + \frac{5}{6 \cdot 5}$

Step 5.9

Multiply $3$ by $10$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{30} - \frac{2 \cdot 10}{30} + \frac{5}{6 \cdot 5}$

Step 5.10

Reorder the factors of $6 \cdot 5$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{30} - \frac{2 \cdot 10}{30} + \frac{5}{5 \cdot 6}$

Step 5.11

Multiply $5$ by $6$ .

$\frac{(x - 4 x \cdot 2) \cdot 3}{30} - \frac{2 \cdot 10}{30} + \frac{5}{30}$

Step 6

Combine the numerators over the common denominator.

$\frac{(x - 4 x \cdot 2) \cdot 3 - 2 \cdot 10 + 5}{30}$

Step 7

Simplify each term.

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Step 7.1

Multiply $2$ by $- 4$ .

$\frac{(x - 8 x) \cdot 3 - 2 \cdot 10 + 5}{30}$

Step 7.2

Subtract $8 x$ from $x$ .

$\frac{- 7 x \cdot 3 - 2 \cdot 10 + 5}{30}$

Step 7.3

Multiply $3$ by $- 7$ .

$\frac{- 21 x - 2 \cdot 10 + 5}{30}$

Step 7.4

Multiply $- 2$ by $10$ .

$\frac{- 21 x - 20 + 5}{30}$

Step 8

Simplify terms.

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Step 8.1

Add $- 20$ and $5$ .

$\frac{- 21 x - 15}{30}$

Step 8.2

Cancel the common factor of $- 21 x - 15$ and $30$ .

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Step 8.2.1

Factor $3$ out of $- 21 x$ .

$\frac{3 (- 7 x) - 15}{30}$

Step 8.2.2

Factor $3$ out of $- 15$ .

$\frac{3 (- 7 x) + 3 (- 5)}{30}$

Step 8.2.3

Factor $3$ out of $3 (- 7 x) + 3 (- 5)$ .

$\frac{3 (- 7 x - 5)}{30}$

Step 8.2.4

Cancel the common factors.

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Step 8.2.4.1

Factor $3$ out of $30$ .

$\frac{3 (- 7 x - 5)}{3 (10)}$

Step 8.2.4.2

Cancel the common factor.

$\frac{3 (- 7 x - 5)}{3 \cdot 10}$

Step 8.2.4.3

Rewrite the expression.

$\frac{- 7 x - 5}{10}$

Step 8.3

Factor $- 1$ out of $- 7 x$ .

$\frac{- (7 x) - 5}{10}$

Step 8.4

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- (7 x) - 1 (5)}{10}$

Step 8.5

Factor $- 1$ out of $- (7 x) - 1 (5)$ .

$\frac{- (7 x + 5)}{10}$

Step 8.6

Simplify the expression.

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Step 8.6.1

Rewrite $- (7 x + 5)$ as $- 1 (7 x + 5)$ .

$\frac{- 1 (7 x + 5)}{10}$

Step 8.6.2

Move the negative in front of the fraction.

$- \frac{7 x + 5}{10}$