Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $6 x$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 1.3

Multiply $2$ by $2$ .

$4 x + \frac{2}{3} (- \frac{1}{6}) + 3 x$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$4 x + \frac{2}{3} \cdot \frac{- 1}{6} + 3 x$

Step 1.4.2

Factor $2$ out of $6$ .

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

Step 1.4.3

Cancel the common factor.

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

Step 1.4.4

Rewrite the expression.

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

Step 1.5

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

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

Step 1.6

Multiply $3$ by $3$ .

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

Step 1.7

Move the negative in front of the fraction.

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

Step 2

Add $4 x$ and $3 x$ .

$7 x - \frac{1}{9}$