1
advanced-math

Solve the inequality: x29<0x^2 - 9 < 0

A

3<x<3-3 < x < 3

B

x<3x < -3 or x>3x > 3

C

x<9x < 9

D

x>3x > 3

Correct Answer: A

Choice A is the correct answer.

  1. Find Roots: Solve x29=0x=±3x^2 - 9 = 0 \Rightarrow x = \pm 3.
  2. Sketch: The parabola y=x29y = x^2 - 9 opens upward.
  3. Test: We want where the graph is below the x-axis (<0< 0).
  4. Result: This occurs between the roots: 3<x<3-3 < x < 3.

Choice B is incorrect because that describes x29>0x^2 - 9 > 0 (outside the roots). Choice C is incorrect. Choice D is incorrect.