1. The problem is to solve the inequality involving $x$ where the solution is given as $x<2$ or $x>3$. 2. This type of inequality typically arises from expressions like $(x-2)(x-3)>0$ or $(x-2)(x-3)<0$. 3. The rule for inequalities involving products is: the product is positive when both factors are positive or both are negative. 4. For $(x-2)(x-3)>0$, the solution is $x<2$ or $x>3$ because: - When $x<2$, both $(x-2)<0$ and $(x-3)<0$, so their product is positive. - When $x>3$, both $(x-2)>0$ and $(x-3)>0$, so their product is positive. 5. Between $2$ and $3$, the product is negative because one factor is positive and the other is negative. 6. Therefore, the solution to the inequality $(x-2)(x-3)>0$ is exactly $x<2$ or $x>3$. Final answer: $x<2$ or $x>3$