# How do you solve 12> -3q and -2q> -12?

Nov 3, 2017

Very carefully! $- 4 < q < 6$

#### Explanation:

You need to be careful when dealing with inequalities and negative coefficients, as multiplying or dividing by a value which might be negative can invalidate the inequality.
The safest method is to add the variable terms to both sides to make their coefficients positive first:
$12 > - 3 q \Rightarrow 12 + 3 q > 0 \Rightarrow 3 q > - 12 \Rightarrow q > - 4$
and:
$- 2 q > - 12 \Rightarrow 0 > 2 q - 12 \Rightarrow 12 > 2 q \Rightarrow 6 > q$
We can combine these two in a single interval:
$- 4 < q < 6$