Answer:
[tex]\huge\boxed{r<12\to x\in(-\infty,\ 12)}[/tex]
Step-by-step explanation:
[tex]\dfrac{3r}{4}<9\ \wedge\ -\dfrac{r}{6}>-3\\\\\dfrac{3r}{4}<9\qquad\text{multiply both sides by 4}\\\\4\!\!\!\!\diagup\cdot\dfrac{3r}{4\!\!\!\!\diagup}<4\cdot9\\\\3r<36\qquad\text{divide both sides by 3}\\\\\dfrac{3r}{3}<\dfrac{36}{3}\\\\\boxed{r<12}\qquad(1)[/tex]
[tex]-\dfrac{r}{6}>-3\qquad\text{change the signs}\\\\\dfrac{r}{6}<3\qquad\text{multiply both sides by 6}\\\\6\!\!\!\!\diagup\cdot\dfrac{r}{6\!\!\!\!\diagup}<6\cdot3\\\\\boxed{r<18}\qquad(2)[/tex]
[tex]\text{From}\ (1)\ \text{and}\ (2)}\ \text{we have}:\\\\r<12\ \wedge\ x<18\Rightarrow\boxed{\boxed{r<12\to x\in(-\infty,\ 12)}}[/tex]
