Algebra Examples

$- 4 a - \frac{3}{2} (- \frac{1}{2} a + 3)$

Step 1

Simplify each term.

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Step 1.1

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

$- 4 a - \frac{3}{2} \cdot (- \frac{a}{2} + 3)$

Step 1.2

Apply the distributive property.

$- 4 a - \frac{3}{2} (- \frac{a}{2}) - \frac{3}{2} \cdot 3$

Step 1.3

Multiply $- \frac{3}{2} (- \frac{a}{2})$ .

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Step 1.3.1

Multiply $- 1$ by $- 1$ .

$- 4 a + 1 (\frac{3}{2}) \frac{a}{2} - \frac{3}{2} \cdot 3$

Step 1.3.2

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

$- 4 a + \frac{3}{2} \cdot \frac{a}{2} - \frac{3}{2} \cdot 3$

Step 1.3.3

Multiply $\frac{3}{2}$ by $\frac{a}{2}$ .

$- 4 a + \frac{3 a}{2 \cdot 2} - \frac{3}{2} \cdot 3$

Step 1.3.4

Multiply $2$ by $2$ .

$- 4 a + \frac{3 a}{4} - \frac{3}{2} \cdot 3$

Step 1.4

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

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Step 1.4.1

Multiply $3$ by $- 1$ .

$- 4 a + \frac{3 a}{4} - 3 (\frac{3}{2})$

Step 1.4.2

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

$- 4 a + \frac{3 a}{4} + \frac{- 3 \cdot 3}{2}$

Step 1.4.3

Multiply $- 3$ by $3$ .

$- 4 a + \frac{3 a}{4} + \frac{- 9}{2}$

Step 1.5

Move the negative in front of the fraction.

$- 4 a + \frac{3 a}{4} - \frac{9}{2}$

Step 2

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

$- 4 a \cdot \frac{4}{4} + \frac{3 a}{4} - \frac{9}{2}$

Step 3

Simplify terms.

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Step 3.1

Combine $- 4 a$ and $\frac{4}{4}$ .

$\frac{- 4 a \cdot 4}{4} + \frac{3 a}{4} - \frac{9}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 4 a \cdot 4 + 3 a}{4} - \frac{9}{2}$

Step 4

Simplify each term.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $a$ out of $- 4 a \cdot 4 + 3 a$ .

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Step 4.1.1.1

Factor $a$ out of $- 4 a \cdot 4$ .

$\frac{a (- 4 \cdot 4) + 3 a}{4} - \frac{9}{2}$

Step 4.1.1.2

Factor $a$ out of $3 a$ .

$\frac{a (- 4 \cdot 4) + a \cdot 3}{4} - \frac{9}{2}$

Step 4.1.1.3

Factor $a$ out of $a (- 4 \cdot 4) + a \cdot 3$ .

$\frac{a (- 4 \cdot 4 + 3)}{4} - \frac{9}{2}$

Step 4.1.2

Multiply $- 4$ by $4$ .

$\frac{a (- 16 + 3)}{4} - \frac{9}{2}$

Step 4.1.3

Add $- 16$ and $3$ .

$\frac{a \cdot - 13}{4} - \frac{9}{2}$

Step 4.2

Move $- 13$ to the left of $a$ .

$\frac{- 13 \cdot a}{4} - \frac{9}{2}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{13 a}{4} - \frac{9}{2}$