We set up the inequality as follows:

`(3q)/(q−3)>12`

The logical first step would be to multiply both sides by (q − 3). However, we can only do that if (q − 3) is positive. (Otherwise, if (q − 3) is negative, the > sign would need to change to `<`.)

Of course, q ≠ 3, since we cannot have `0` on the bottom of a fraction.

So we have (if q > 3):

3q > 12(q − 3)

Divide both sides by 3:

q > 4(q − 3)

Expand brackets:

q > 4q − 12

Add 12 to both sides and subtract q from both sides:

12 > 4qq

12 > 3q

4 > q

Reverse sides (and reversing the > sign as well):

q < 4

So including the condition q > 3, our final answer is:

3 < q < 4

The graph of the solution:

1234560-1qOpen image in a new page

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