Complete the table below - Edexcel - A-Level Maths Pure - Question 8 - 2017 - Paper 2

This statement is Sometimes True. If we assume $a > 0$, then dividing by $a$ maintains the inequality, resulting in: $ax > b \Rightarrow x > \frac{b}{a}$ However, if $a < 0$, dividing by $a$ reverses the inequality, and we cannot guarantee that $x > \frac{b}{a}$. Hence, it is not always true.

Let the consecutive square numbers be represented as $n^2$ and $(n+1)^2$. The difference is: $(n+1)^2 - n^2 = 2n + 1$ Since $2n$ is even for any integer $n$, adding 1 makes $2n + 1$ always odd. Therefore, this statement is Always True.