Algebra Examples

$\frac{1}{2} (2 x + 4) - \frac{1}{3} (9 x - 6)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot 4 - \frac{1}{3} \cdot (9 x - 6)$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) + \frac{1}{2} \cdot 4 - \frac{1}{3} \cdot (9 x - 6)$

Step 1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) + \frac{1}{2} \cdot 4 - \frac{1}{3} \cdot (9 x - 6)$

Step 1.2.3

Rewrite the expression.

$x + \frac{1}{2} \cdot 4 - \frac{1}{3} \cdot (9 x - 6)$

Step 1.3

Cancel the common factor of $2$ .

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Step 1.3.1

Factor $2$ out of $4$ .

$x + \frac{1}{2} \cdot (2 (2)) - \frac{1}{3} \cdot (9 x - 6)$

Step 1.3.2

Cancel the common factor.

$x + \frac{1}{2} \cdot (2 \cdot 2) - \frac{1}{3} \cdot (9 x - 6)$

Step 1.3.3

Rewrite the expression.

$x + 2 - \frac{1}{3} \cdot (9 x - 6)$

Step 1.4

Apply the distributive property.

$x + 2 - \frac{1}{3} (9 x) - \frac{1}{3} \cdot - 6$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$x + 2 + \frac{- 1}{3} (9 x) - \frac{1}{3} \cdot - 6$

Step 1.5.2

Factor $3$ out of $9 x$ .

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

Step 1.5.3

Cancel the common factor.

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

Step 1.5.4

Rewrite the expression.

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

Step 1.6

Multiply $3$ by $- 1$ .

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

Step 1.7

Cancel the common factor of $3$ .

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Step 1.7.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

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

Step 1.7.2

Factor $3$ out of $- 6$ .

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

Step 1.7.3

Cancel the common factor.

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

Step 1.7.4

Rewrite the expression.

$x + 2 - 3 x - 1 \cdot - 2$

Step 1.8

Multiply $- 1$ by $- 2$ .

$x + 2 - 3 x + 2$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $3 x$ from $x$ .

$- 2 x + 2 + 2$

Step 2.2

Add $2$ and $2$ .

$- 2 x + 4$