Algebra Examples

$\frac{1}{2} (\frac{3}{5} x - 8) + \frac{7}{4} (\frac{2}{5} x + 4)$

Step 1

Simplify each term.

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Step 1.1

Combine $\frac{3}{5}$ and $x$ .

$\frac{1}{2} \cdot (\frac{3 x}{5} - 8) + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Step 1.2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{1}{2} \cdot (\frac{3 x}{5} - 8 \cdot \frac{5}{5}) + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Step 1.3

Combine $- 8$ and $\frac{5}{5}$ .

$\frac{1}{2} \cdot (\frac{3 x}{5} + \frac{- 8 \cdot 5}{5}) + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Step 1.4

Combine the numerators over the common denominator.

$\frac{1}{2} \cdot \frac{3 x - 8 \cdot 5}{5} + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Step 1.5

Multiply $- 8$ by $5$ .

$\frac{1}{2} \cdot \frac{3 x - 40}{5} + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Step 1.6

Multiply $\frac{1}{2} \cdot \frac{3 x - 40}{5}$ .

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Step 1.6.1

Multiply $\frac{1}{2}$ by $\frac{3 x - 40}{5}$ .

$\frac{3 x - 40}{2 \cdot 5} + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Step 1.6.2

Multiply $2$ by $5$ .

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Step 1.7

Combine $\frac{2}{5}$ and $x$ .

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot (\frac{2 x}{5} + 4)$

Step 1.8

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

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot (\frac{2 x}{5} + 4 \cdot \frac{5}{5})$

Step 1.9

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

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot (\frac{2 x}{5} + \frac{4 \cdot 5}{5})$

Step 1.10

Combine the numerators over the common denominator.

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot \frac{2 x + 4 \cdot 5}{5}$

Step 1.11

Simplify the numerator.

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Step 1.11.1

Factor $2$ out of $2 x + 4 \cdot 5$ .

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Step 1.11.1.1

Factor $2$ out of $2 x$ .

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot \frac{2 (x) + 4 \cdot 5}{5}$

Step 1.11.1.2

Factor $2$ out of $4 \cdot 5$ .

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot \frac{2 (x) + 2 (2 \cdot 5)}{5}$

Step 1.11.1.3

Factor $2$ out of $2 (x) + 2 (2 \cdot 5)$ .

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot \frac{2 (x + 2 \cdot 5)}{5}$

Step 1.11.2

Multiply $2$ by $5$ .

$\frac{3 x - 40}{10} + \frac{7}{4} \cdot \frac{2 (x + 10)}{5}$

Step 1.12

Cancel the common factor of $2$ .

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Step 1.12.1

Factor $2$ out of $4$ .

$\frac{3 x - 40}{10} + \frac{7}{2 (2)} \cdot \frac{2 (x + 10)}{5}$

Step 1.12.2

Cancel the common factor.

$\frac{3 x - 40}{10} + \frac{7}{2 \cdot 2} \cdot \frac{2 (x + 10)}{5}$

Step 1.12.3

Rewrite the expression.

$\frac{3 x - 40}{10} + \frac{7}{2} \cdot \frac{x + 10}{5}$

Step 1.13

Multiply $\frac{7}{2}$ by $\frac{x + 10}{5}$ .

$\frac{3 x - 40}{10} + \frac{7 (x + 10)}{2 \cdot 5}$

Step 1.14

Multiply $2$ by $5$ .

$\frac{3 x - 40}{10} + \frac{7 (x + 10)}{10}$

Step 2

Combine the numerators over the common denominator.

$\frac{3 x - 40 + 7 (x + 10)}{10}$

Step 3

Simplify each term.

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Step 3.1

Apply the distributive property.

$\frac{3 x - 40 + 7 x + 7 \cdot 10}{10}$

Step 3.2

Multiply $7$ by $10$ .

$\frac{3 x - 40 + 7 x + 70}{10}$

Step 4

Simplify terms.

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Step 4.1

Add $3 x$ and $7 x$ .

$\frac{10 x - 40 + 70}{10}$

Step 4.2

Add $- 40$ and $70$ .

$\frac{10 x + 30}{10}$

Step 4.3

Cancel the common factor of $10 x + 30$ and $10$ .

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Step 4.3.1

Factor $10$ out of $10 x$ .

$\frac{10 (x) + 30}{10}$

Step 4.3.2

Factor $10$ out of $30$ .

$\frac{10 (x) + 10 \cdot 3}{10}$

Step 4.3.3

Factor $10$ out of $10 (x) + 10 (3)$ .

$\frac{10 (x + 3)}{10}$

Step 4.3.4

Cancel the common factors.

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Step 4.3.4.1

Factor $10$ out of $10$ .

$\frac{10 (x + 3)}{10 (1)}$

Step 4.3.4.2

Cancel the common factor.

$\frac{10 (x + 3)}{10 \cdot 1}$

Step 4.3.4.3

Rewrite the expression.

$\frac{x + 3}{1}$

Step 4.3.4.4

Divide $x + 3$ by $1$ .

$x + 3$