Algebra Examples

$(- \frac{1}{2} x + \frac{7}{10}) - (- \frac{3}{4} x - \frac{1}{5})$

Step 1

Simplify each term.

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Step 1.1

Combine $x$ and $\frac{1}{2}$ .

$- \frac{x}{2} + \frac{7}{10} - (- \frac{3}{4} x - \frac{1}{5})$

Step 1.2

Simplify each term.

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Step 1.2.1

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

$- \frac{x}{2} + \frac{7}{10} - (- \frac{x \cdot 3}{4} - \frac{1}{5})$

Step 1.2.2

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

$- \frac{x}{2} + \frac{7}{10} - (- \frac{3 x}{4} - \frac{1}{5})$

Step 1.3

Apply the distributive property.

$- \frac{x}{2} + \frac{7}{10} - - \frac{3 x}{4} - - \frac{1}{5}$

Step 1.4

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

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Step 1.4.1

Multiply $- 1$ by $- 1$ .

$- \frac{x}{2} + \frac{7}{10} + 1 \frac{3 x}{4} - - \frac{1}{5}$

Step 1.4.2

Multiply $\frac{3 x}{4}$ by $1$ .

$- \frac{x}{2} + \frac{7}{10} + \frac{3 x}{4} - - \frac{1}{5}$

Step 1.5

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

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Step 1.5.1

Multiply $- 1$ by $- 1$ .

$- \frac{x}{2} + \frac{7}{10} + \frac{3 x}{4} + 1 (\frac{1}{5})$

Step 1.5.2

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

$- \frac{x}{2} + \frac{7}{10} + \frac{3 x}{4} + \frac{1}{5}$

Step 2

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

$- \frac{x}{2} \cdot \frac{2}{2} + \frac{3 x}{4} + \frac{7}{10} + \frac{1}{5}$

Step 3

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.1

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

$- \frac{x \cdot 2}{2 \cdot 2} + \frac{3 x}{4} + \frac{7}{10} + \frac{1}{5}$

Step 3.2

Multiply $2$ by $2$ .

$- \frac{x \cdot 2}{4} + \frac{3 x}{4} + \frac{7}{10} + \frac{1}{5}$

Step 4

Combine the numerators over the common denominator.

$\frac{- x \cdot 2 + 3 x}{4} + \frac{7}{10} + \frac{1}{5}$

Step 5

Find the common denominator.

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Step 5.1

Multiply $\frac{- x \cdot 2 + 3 x}{4}$ by $\frac{5}{5}$ .

$\frac{- x \cdot 2 + 3 x}{4} \cdot \frac{5}{5} + \frac{7}{10} + \frac{1}{5}$

Step 5.2

Multiply $\frac{- x \cdot 2 + 3 x}{4}$ by $\frac{5}{5}$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{4 \cdot 5} + \frac{7}{10} + \frac{1}{5}$

Step 5.3

Multiply $\frac{7}{10}$ by $\frac{2}{2}$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{4 \cdot 5} + \frac{7}{10} \cdot \frac{2}{2} + \frac{1}{5}$

Step 5.4

Multiply $\frac{7}{10}$ by $\frac{2}{2}$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{4 \cdot 5} + \frac{7 \cdot 2}{10 \cdot 2} + \frac{1}{5}$

Step 5.5

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{4 \cdot 5} + \frac{7 \cdot 2}{10 \cdot 2} + \frac{1}{5} \cdot \frac{4}{4}$

Step 5.6

Multiply $\frac{1}{5}$ by $\frac{4}{4}$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{4 \cdot 5} + \frac{7 \cdot 2}{10 \cdot 2} + \frac{4}{5 \cdot 4}$

Step 5.7

Multiply $4$ by $5$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{20} + \frac{7 \cdot 2}{10 \cdot 2} + \frac{4}{5 \cdot 4}$

Step 5.8

Reorder the factors of $10 \cdot 2$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{20} + \frac{7 \cdot 2}{2 \cdot 10} + \frac{4}{5 \cdot 4}$

Step 5.9

Multiply $2$ by $10$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{20} + \frac{7 \cdot 2}{20} + \frac{4}{5 \cdot 4}$

Step 5.10

Reorder the factors of $5 \cdot 4$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{20} + \frac{7 \cdot 2}{20} + \frac{4}{4 \cdot 5}$

Step 5.11

Multiply $4$ by $5$ .

$\frac{(- x \cdot 2 + 3 x) \cdot 5}{20} + \frac{7 \cdot 2}{20} + \frac{4}{20}$

Step 6

Combine the numerators over the common denominator.

$\frac{(- x \cdot 2 + 3 x) \cdot 5 + 7 \cdot 2 + 4}{20}$

Step 7

Simplify each term.

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Step 7.1

Multiply $2$ by $- 1$ .

$\frac{(- 2 x + 3 x) \cdot 5 + 7 \cdot 2 + 4}{20}$

Step 7.2

Add $- 2 x$ and $3 x$ .

$\frac{x \cdot 5 + 7 \cdot 2 + 4}{20}$

Step 7.3

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

$\frac{5 \cdot x + 7 \cdot 2 + 4}{20}$

Step 7.4

Multiply $7$ by $2$ .

$\frac{5 x + 14 + 4}{20}$

Step 8

Add $14$ and $4$ .

$\frac{5 x + 18}{20}$