Algebra Examples

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

Step 1

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

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

Step 2

Simplify terms.

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Step 2.1

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

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

Step 2.2

Combine the numerators over the common denominator.

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

Step 3

Simplify the numerator.

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Step 3.1

Multiply $2$ by $- 3$ .

$\frac{x + 6 - 6 x}{2}$

Step 3.2

Subtract $6 x$ from $x$ .

$\frac{- 5 x + 6}{2}$

Step 4

Simplify with factoring out.

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Step 4.1

Factor $- 1$ out of $- 5 x$ .

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

Step 4.2

Rewrite $6$ as $- 1 (- 6)$ .

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

Step 4.3

Factor $- 1$ out of $- (5 x) - 1 (- 6)$ .

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

Step 4.4

Simplify the expression.

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Step 4.4.1

Rewrite $- (5 x - 6)$ as $- 1 (5 x - 6)$ .

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

Step 4.4.2

Move the negative in front of the fraction.

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