Algebra Examples

$- \frac{1}{2} (- \frac{3}{2} x + 6 x + 1) - 3 x$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

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

$- \frac{1}{2} \cdot (- \frac{x \cdot 3}{2} + 6 x + 1) - 3 x$

Step 1.1.2

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

$- \frac{1}{2} \cdot (- \frac{3 x}{2} + 6 x + 1) - 3 x$

Step 1.2

To write $6 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{1}{2} \cdot (- \frac{3 x}{2} + 6 x \cdot \frac{2}{2} + 1) - 3 x$

Step 1.3

Combine $6 x$ and $\frac{2}{2}$ .

$- \frac{1}{2} \cdot (- \frac{3 x}{2} + \frac{6 x \cdot 2}{2} + 1) - 3 x$

Step 1.4

Combine the numerators over the common denominator.

$- \frac{1}{2} \cdot (\frac{- 3 x + 6 x \cdot 2}{2} + 1) - 3 x$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Factor $3 x$ out of $- 3 x + 6 x \cdot 2$ .

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Step 1.5.1.1

Factor $3 x$ out of $- 3 x$ .

$- \frac{1}{2} \cdot (\frac{3 x (- 1) + 6 x \cdot 2}{2} + 1) - 3 x$

Step 1.5.1.2

Factor $3 x$ out of $6 x \cdot 2$ .

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

Step 1.5.1.3

Factor $3 x$ out of $3 x (- 1) + 3 x (2 \cdot 2)$ .

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

Step 1.5.2

Multiply $2$ by $2$ .

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

Step 1.5.3

Add $- 1$ and $4$ .

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

Step 1.5.4

Multiply $3$ by $3$ .

$- \frac{1}{2} \cdot (\frac{9 x}{2} + 1) - 3 x$

Step 1.6

Apply the distributive property.

$- \frac{1}{2} \cdot \frac{9 x}{2} - \frac{1}{2} \cdot 1 - 3 x$

Step 1.7

Multiply $- \frac{1}{2} \cdot \frac{9 x}{2}$ .

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Step 1.7.1

Multiply $\frac{9 x}{2}$ by $\frac{1}{2}$ .

$- \frac{9 x}{2 \cdot 2} - \frac{1}{2} \cdot 1 - 3 x$

Step 1.7.2

Multiply $2$ by $2$ .

$- \frac{9 x}{4} - \frac{1}{2} \cdot 1 - 3 x$

Step 1.8

Multiply $- 1$ by $1$ .

$- \frac{9 x}{4} - \frac{1}{2} - 3 x$

Step 2

To write $- 3 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$- \frac{9 x}{4} - 3 x \cdot \frac{4}{4} - \frac{1}{2}$

Step 3

Simplify terms.

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Step 3.1

Combine $- 3 x$ and $\frac{4}{4}$ .

$- \frac{9 x}{4} + \frac{- 3 x \cdot 4}{4} - \frac{1}{2}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- 9 x - 3 x \cdot 4}{4} - \frac{1}{2}$

Step 4

Simplify each term.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Factor $3 x$ out of $- 9 x - 3 x \cdot 4$ .

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Step 4.1.1.1

Factor $3 x$ out of $- 9 x$ .

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

Step 4.1.1.2

Factor $3 x$ out of $- 3 x \cdot 4$ .

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

Step 4.1.1.3

Factor $3 x$ out of $3 x (- 3) + 3 x (- 1 \cdot 4)$ .

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

Step 4.1.2

Multiply $- 1$ by $4$ .

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

Step 4.1.3

Subtract $4$ from $- 3$ .

$\frac{3 x \cdot - 7}{4} - \frac{1}{2}$

Step 4.1.4

Multiply $- 7$ by $3$ .

$\frac{- 21 x}{4} - \frac{1}{2}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{21 x}{4} - \frac{1}{2}$