Question

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

Answer 1

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 > -3q rArr 12+3q > 0 rArr 3q > -12 rArr q > -4`
and:
`-2q > -12 rArr 0 > 2q-12 rArr 12 > 2q rArr 6 > q`
We can combine these two in a single interval:
`-4 < q < 6`