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):

3

q> 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 > 4

q−q12 > 3

q4 >

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:

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