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

Apply the distributive property.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $5$ .

$\frac{3 x}{10} + \frac{1}{2} \cdot - 8 + \frac{7}{4} \cdot (\frac{2}{5} x + 4)$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $- 8$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 1.5

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

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

Step 1.6

Apply the distributive property.

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

Step 1.7

Cancel the common factor of $2$ .

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Step 1.7.1

Factor $2$ out of $4$ .

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

Step 1.7.2

Factor $2$ out of $2 x$ .

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

Step 1.7.3

Cancel the common factor.

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

Step 1.7.4

Rewrite the expression.

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

Step 1.8

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

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

Step 1.9

Multiply $2$ by $5$ .

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

Step 1.10

Cancel the common factor of $4$ .

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Step 1.10.1

Cancel the common factor.

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

Step 1.10.2

Rewrite the expression.

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

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

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

Step 2.2

Add $3 x$ and $7 x$ .

$- 4 + 7 + \frac{10 x}{10}$

Step 2.3

Cancel the common factor of $10$ .

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Step 2.3.1

Cancel the common factor.

$- 4 + 7 + \frac{10 x}{10}$

Step 2.3.2

Divide $x$ by $1$ .

$- 4 + 7 + x$

Step 2.4

Add $- 4$ and $7$ .

$3 + x$