2. Provide a counterexample to disprove the statement:
If x
2 > 4, then x > 2.

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.

Provide a counterexample to disprove the statement: If x^2 > 4, then x > 2.

Discover how to disprove the statement 'If x^2 > 4, then x > 2' with a clear counterexample. This solution involves quadratic functions and inequalities, suitable for students in Grades 8-10.

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