Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

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

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

Step 1.3

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

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Step 1.3.1

Multiply $2$ by $- 1$ .

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

Step 1.3.2

Combine $- 2$ and $\frac{4}{3}$ .

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

Step 1.3.3

Multiply $- 2$ by $4$ .

$- \frac{3}{2} - \frac{x \cdot 4}{3} + \frac{- 8}{3}$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$- \frac{3}{2} - \frac{4 \cdot x}{3} + \frac{- 8}{3}$

Step 1.4.2

Move the negative in front of the fraction.

$- \frac{3}{2} - \frac{4 x}{3} - \frac{8}{3}$

Step 2

To write $- \frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$- \frac{4 x}{3} - \frac{3}{2} \cdot \frac{3}{3} - \frac{8}{3}$

Step 3

To write $- \frac{8}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- \frac{4 x}{3} - \frac{3}{2} \cdot \frac{3}{3} - \frac{8}{3} \cdot \frac{2}{2}$

Step 4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

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

$- \frac{4 x}{3} - \frac{3 \cdot 3}{2 \cdot 3} - \frac{8}{3} \cdot \frac{2}{2}$

Step 4.2

Multiply $2$ by $3$ .

$- \frac{4 x}{3} - \frac{3 \cdot 3}{6} - \frac{8}{3} \cdot \frac{2}{2}$

Step 4.3

Multiply $\frac{8}{3}$ by $\frac{2}{2}$ .

$- \frac{4 x}{3} - \frac{3 \cdot 3}{6} - \frac{8 \cdot 2}{3 \cdot 2}$

Step 4.4

Multiply $3$ by $2$ .

$- \frac{4 x}{3} - \frac{3 \cdot 3}{6} - \frac{8 \cdot 2}{6}$

Step 5

Combine the numerators over the common denominator.

$- \frac{4 x}{3} + \frac{- 3 \cdot 3 - 8 \cdot 2}{6}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $- 3$ by $3$ .

$- \frac{4 x}{3} + \frac{- 9 - 8 \cdot 2}{6}$

Step 6.2

Multiply $- 8$ by $2$ .

$- \frac{4 x}{3} + \frac{- 9 - 16}{6}$

Step 6.3

Subtract $16$ from $- 9$ .

$- \frac{4 x}{3} + \frac{- 25}{6}$

Step 7

Move the negative in front of the fraction.

$- \frac{4 x}{3} - \frac{25}{6}$