Algebra Examples

$\frac{7}{8} (\frac{4}{5} x + 16) + \frac{3}{5} (\frac{1}{2} x - 10)$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{7}{8} \cdot (\frac{4 x}{5} + 16) + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.2

Apply the distributive property.

$\frac{7}{8} \cdot \frac{4 x}{5} + \frac{7}{8} \cdot 16 + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $8$ .

$\frac{7}{4 (2)} \cdot \frac{4 x}{5} + \frac{7}{8} \cdot 16 + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.3.2

Factor $4$ out of $4 x$ .

$\frac{7}{4 (2)} \cdot \frac{4 (x)}{5} + \frac{7}{8} \cdot 16 + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.3.3

Cancel the common factor.

$\frac{7}{4 \cdot 2} \cdot \frac{4 x}{5} + \frac{7}{8} \cdot 16 + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.3.4

Rewrite the expression.

$\frac{7}{2} \cdot \frac{x}{5} + \frac{7}{8} \cdot 16 + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.4

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

$\frac{7 x}{2 \cdot 5} + \frac{7}{8} \cdot 16 + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.5

Multiply $2$ by $5$ .

$\frac{7 x}{10} + \frac{7}{8} \cdot 16 + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.6

Cancel the common factor of $8$ .

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Step 1.6.1

Factor $8$ out of $16$ .

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

Step 1.6.2

Cancel the common factor.

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

Step 1.6.3

Rewrite the expression.

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

Step 1.7

Multiply $7$ by $2$ .

$\frac{7 x}{10} + 14 + \frac{3}{5} \cdot (\frac{1}{2} x - 10)$

Step 1.8

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

$\frac{7 x}{10} + 14 + \frac{3}{5} \cdot (\frac{x}{2} - 10)$

Step 1.9

Apply the distributive property.

$\frac{7 x}{10} + 14 + \frac{3}{5} \cdot \frac{x}{2} + \frac{3}{5} \cdot - 10$

Step 1.10

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

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Step 1.10.1

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

$\frac{7 x}{10} + 14 + \frac{3 x}{5 \cdot 2} + \frac{3}{5} \cdot - 10$

Step 1.10.2

Multiply $5$ by $2$ .

$\frac{7 x}{10} + 14 + \frac{3 x}{10} + \frac{3}{5} \cdot - 10$

Step 1.11

Cancel the common factor of $5$ .

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Step 1.11.1

Factor $5$ out of $- 10$ .

$\frac{7 x}{10} + 14 + \frac{3 x}{10} + \frac{3}{5} \cdot (5 (- 2))$

Step 1.11.2

Cancel the common factor.

$\frac{7 x}{10} + 14 + \frac{3 x}{10} + \frac{3}{5} \cdot (5 \cdot - 2)$

Step 1.11.3

Rewrite the expression.

$\frac{7 x}{10} + 14 + \frac{3 x}{10} + 3 \cdot - 2$

Step 1.12

Multiply $3$ by $- 2$ .

$\frac{7 x}{10} + 14 + \frac{3 x}{10} - 6$

Step 2

Simplify terms.

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Step 2.1

Combine the numerators over the common denominator.

$14 - 6 + \frac{7 x + 3 x}{10}$

Step 2.2

Add $7 x$ and $3 x$ .

$14 - 6 + \frac{10 x}{10}$

Step 2.3

Cancel the common factor of $10$ .

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Step 2.3.1

Cancel the common factor.

$14 - 6 + \frac{10 x}{10}$

Step 2.3.2

Divide $x$ by $1$ .

$14 - 6 + x$

Step 2.4

Subtract $6$ from $14$ .

$8 + x$