Simplify (x+12)/2-2x

$\frac{x + 12}{2} - 2 x$

Step 1

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

$\frac{x + 12}{2} - 2 x \cdot \frac{2}{2}$

Step 2

Simplify terms.

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

$\frac{x + 12}{2} + \frac{- 2 x \cdot 2}{2}$

Combine the numerators over the common denominator.

$\frac{x + 12 - 2 x \cdot 2}{2}$

Step 3

Simplify the numerator.

Multiply $2$ by $- 2$ .

$\frac{x + 12 - 4 x}{2}$

Subtract $4 x$ from $x$ .

$\frac{- 3 x + 12}{2}$

Factor $3$ out of $- 3 x + 12$ .

Factor $3$ out of $- 3 x$ .

$\frac{3 (- x) + 12}{2}$

Factor $3$ out of $12$ .

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

Factor $3$ out of $3 (- x) + 3 (4)$ .

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

Step 4

Simplify with factoring out.

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

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

Rewrite $4$ as $- 1 (- 4)$ .

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

Factor $- 1$ out of $- (x) - 1 (- 4)$ .

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

Simplify the expression.

Rewrite $- (x - 4)$ as $- 1 (x - 4)$ .

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

Move the negative in front of the fraction.

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