The statement "If $x^2 > 4$, then $x > 2$" is false, and here’s a counterexample to disprove it:

Let $x = -3$.

• If $x = -3$, then: $x^2 = (-3)^2 = 9.$ Since $9 > 4$, it is true that $x^2 > 4$.

• However, $x = -3$, and $-3$ is not greater than $2$. In fact, $-3 < 2$.

Thus, the statement "If $x^2 > 4$, then $x > 2$" is false because $x = -3$ satisfies $x^2 > 4$, but does not satisfy $x > 2$.

Would you like more details or have any other questions?

Here are 5 related questions:

1. Can you provide another counterexample for this statement?
2. What would be the correct conclusion for $x^2 > 4$?
3. How do we solve inequalities involving absolute values?
4. Can $x^2$ ever be negative?
5. How does squaring a number affect its sign?

Tip: When dealing with squared terms, always remember that both positive and negative numbers can result in the same squared value.