1. Solve $(x-2)(x+3)>0$.

Answer: $x<-3$ or $x>2$

2. Solve $(x-1)(x-5)<0$.

Answer: $1<x<5$

3. Solve $x^2-9\geq0$.

Answer: $x\leq-3$ or $x\geq3$

4. Solve $-x^2+4>0$.

Answer: $-2<x<2$

5. Solve $x^2+x-6\leq0$.

Answer: $-3\leq x\leq2$

6. Solve $2x^2-8x>0$.

Answer: $x<0$ or $x>4$

7. Solve $(x+4)(x-1)\leq0$.

Answer: $-4\leq x\leq1$

8. Which method applies, and why? Solve $x^2-4x+3>0$.

Answer: 'Factor the quadratic: $(x-1)(x-3)>0$, so $x<1$ or $x>3$.'

9. Solve $x^2-5x+6<0$.

Answer: $2<x<3$