Algebra Examples

$- \frac{2}{3} (\frac{5}{6} x - 3)$

Step 1

Combine $\frac{5}{6}$ and $x$ .

$- \frac{2}{3} \cdot (\frac{5 x}{6} - 3)$

Step 2

Apply the distributive property.

$- \frac{2}{3} \cdot \frac{5 x}{6} - \frac{2}{3} \cdot - 3$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} \cdot \frac{5 x}{6} - \frac{2}{3} \cdot - 3$

Step 3.2

Factor $2$ out of $- 2$ .

$\frac{2 (- 1)}{3} \cdot \frac{5 x}{6} - \frac{2}{3} \cdot - 3$

Step 3.3

Factor $2$ out of $6$ .

$\frac{2 \cdot - 1}{3} \cdot \frac{5 x}{2 \cdot 3} - \frac{2}{3} \cdot - 3$

Step 3.4

Cancel the common factor.

$\frac{2 \cdot - 1}{3} \cdot \frac{5 x}{2 \cdot 3} - \frac{2}{3} \cdot - 3$

Step 3.5

Rewrite the expression.

$\frac{- 1}{3} \cdot \frac{5 x}{3} - \frac{2}{3} \cdot - 3$

Step 4

Multiply $\frac{- 1}{3}$ by $\frac{5 x}{3}$ .

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

Step 5

Multiply.

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Step 5.1

Multiply $5$ by $- 1$ .

$\frac{- 5 x}{3 \cdot 3} - \frac{2}{3} \cdot - 3$

Step 5.2

Multiply $3$ by $3$ .

$\frac{- 5 x}{9} - \frac{2}{3} \cdot - 3$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 5 x}{9} + \frac{- 2}{3} \cdot - 3$

Step 6.2

Factor $3$ out of $- 3$ .

$\frac{- 5 x}{9} + \frac{- 2}{3} \cdot (3 (- 1))$

Step 6.3

Cancel the common factor.

$\frac{- 5 x}{9} + \frac{- 2}{3} \cdot (3 \cdot - 1)$

Step 6.4

Rewrite the expression.

$\frac{- 5 x}{9} - 2 \cdot - 1$

Step 7

Simplify the expression.

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Step 7.1

Multiply $- 2$ by $- 1$ .

$\frac{- 5 x}{9} + 2$

Step 7.2

Move the negative in front of the fraction.

$- \frac{5 x}{9} + 2$