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

Apply the distributive property.

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

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Cancel the common factor.

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

Step 1.2.2

Rewrite the expression.

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

Step 1.3

Multiply $2$ by $- 5$ .

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

Step 1.4

Apply the distributive property.

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

Step 1.5

Combine $x$ and $\frac{3}{2}$ .

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

Step 1.6

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

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Step 1.6.1

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

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

Step 1.6.2

Multiply $7$ by $3$ .

$x - 10 - \frac{x \cdot 3}{2} - \frac{21}{4 \cdot 2}$

Step 1.6.3

Multiply $4$ by $2$ .

$x - 10 - \frac{x \cdot 3}{2} - \frac{21}{8}$

Step 1.7

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

$x - 10 - \frac{3 x}{2} - \frac{21}{8}$

Step 2

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

$x \cdot \frac{2}{2} - \frac{3 x}{2} - 10 - \frac{21}{8}$

Step 3

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

$\frac{x \cdot 2}{2} - \frac{3 x}{2} - 10 - \frac{21}{8}$

Step 4

Combine the numerators over the common denominator.

$\frac{x \cdot 2 - 3 x}{2} - 10 - \frac{21}{8}$

Step 5

Subtract $3 x$ from $x \cdot 2$ .

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Step 5.1

Reorder $x$ and $2$ .

$\frac{2 \cdot x - 3 x}{2} - 10 - \frac{21}{8}$

Step 5.2

Subtract $3 x$ from $2 \cdot x$ .

$\frac{- x}{2} - 10 - \frac{21}{8}$

Step 6

Move the negative in front of the fraction.

$- \frac{x}{2} - 10 - \frac{21}{8}$

Step 7

To write $- 10$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{x}{2} - 10 \cdot \frac{8}{8} - \frac{21}{8}$

Step 8

Combine $- 10$ and $\frac{8}{8}$ .

$- \frac{x}{2} + \frac{- 10 \cdot 8}{8} - \frac{21}{8}$

Step 9

Combine the numerators over the common denominator.

$- \frac{x}{2} + \frac{- 10 \cdot 8 - 21}{8}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $- 10$ by $8$ .

$- \frac{x}{2} + \frac{- 80 - 21}{8}$

Step 10.2

Subtract $21$ from $- 80$ .

$- \frac{x}{2} + \frac{- 101}{8}$

Step 11

Move the negative in front of the fraction.

$- \frac{x}{2} - \frac{101}{8}$