# How do you solve 14<= -x/2?

Jun 7, 2016

$x \le - 28$

#### Explanation:

The issue in this example is the fact that the x-term is negative.
In working with inequalities, if you divide or multiply by a negative number, the inequality sign in the middle changes around.
It is better to avoid the problem altogether by moving the x term to the other side. As this is done by ADDING to both sides, there is not a problem.
$14 \le - \frac{x}{2} \text{ can be changed to } \frac{x}{2} \le - 14$

Now, multiply both sides by 2 to get $x \le - 28$

The other method would be as follows:
$14 \le - \frac{x}{2} \text{ multiply both sides by -2}$

$- 2 \times 14 \ge - \frac{x}{2} \times - 2 \text{ note the sign change in the middle}$
$- 28 \ge x$
This can be written better as $x \le - 28$