5

Set 5: Linear Inequalities (Intermediate)

Explanation

Answer: A

Solve: x2<9x^2 < 9 (Non-linear preview)

A.

3<x<3-3 < x < 3

✓ Correct
B.

x<3x < 3

C.

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

D.

x>3x > 3

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Square root property. 1. Logic: Numbers whose square is less than 9 are between -3 and 3 (e.g., 0, 2, -2). 2. Algebra: x<33<x<3|x| < 3 \rightarrow -3 < x < 3 Strategic Tip: x2<a2x^2 < a^2 is equivalent to a<x<a-a < x < a. Choice B is incorrect because it includes large negative numbers (e.g., -10) whose square is >9>9. Choice C is incorrect because it describes x2>9x^2 > 9. Choice D is incorrect because it misses negative solutions.

Key Steps:

The correct answer is 3<x<3-3 < x < 3

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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