Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Multiply $- 5$ by $2$ .

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

Step 1.5

Cancel the common factor of $2$ .

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Step 1.5.1

Cancel the common factor.

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

Step 1.5.2

Rewrite the expression.

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

Step 1.6

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

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

Step 1.7

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

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

Step 1.8

Combine the numerators over the common denominator.

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

Step 1.9

Move $4$ to the left of $x$ .

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

Step 1.10

Multiply $- \frac{3}{2} \cdot \frac{4 x + 7}{4}$ .

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Step 1.10.1

Multiply $\frac{4 x + 7}{4}$ by $\frac{3}{2}$ .

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

Step 1.10.2

Multiply $4$ by $2$ .

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

Step 1.11

Move $3$ to the left of $4 x + 7$ .

$x - 10 - \frac{3 (4 x + 7)}{8}$

Step 2

Find the common denominator.

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Step 2.1

Write $x$ as a fraction with denominator $1$ .

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

Step 2.2

Multiply $\frac{x}{1}$ by $\frac{8}{8}$ .

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

Step 2.3

Multiply $\frac{x}{1}$ by $\frac{8}{8}$ .

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

Step 2.4

Write $- 10$ as a fraction with denominator $1$ .

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

Step 2.5

Multiply $\frac{- 10}{1}$ by $\frac{8}{8}$ .

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

Step 2.6

Multiply $\frac{- 10}{1}$ by $\frac{8}{8}$ .

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify each term.

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Step 4.1

Move $8$ to the left of $x$ .

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

Step 4.2

Multiply $- 10$ by $8$ .

$\frac{8 x - 80 - 3 (4 x + 7)}{8}$

Step 4.3

Apply the distributive property.

$\frac{8 x - 80 - 3 (4 x) - 3 \cdot 7}{8}$

Step 4.4

Multiply $4$ by $- 3$ .

$\frac{8 x - 80 - 12 x - 3 \cdot 7}{8}$

Step 4.5

Multiply $- 3$ by $7$ .

$\frac{8 x - 80 - 12 x - 21}{8}$

Step 5

Simplify terms.

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Step 5.1

Subtract $12 x$ from $8 x$ .

$\frac{- 4 x - 80 - 21}{8}$

Step 5.2

Subtract $21$ from $- 80$ .

$\frac{- 4 x - 101}{8}$

Step 5.3

Factor $- 1$ out of $- 4 x$ .

$\frac{- (4 x) - 101}{8}$

Step 5.4

Rewrite $- 101$ as $- 1 (101)$ .

$\frac{- (4 x) - 1 (101)}{8}$

Step 5.5

Factor $- 1$ out of $- (4 x) - 1 (101)$ .

$\frac{- (4 x + 101)}{8}$

Step 5.6

Simplify the expression.

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Step 5.6.1

Rewrite $- (4 x + 101)$ as $- 1 (4 x + 101)$ .

$\frac{- 1 (4 x + 101)}{8}$

Step 5.6.2

Move the negative in front of the fraction.

$- \frac{4 x + 101}{8}$