What is the solution set for the inequality: x^2 - 4 < 0?

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Question: What is the solution set for the inequality: x^2 - 4 < 0?

Options:

Correct Answer: (-2, 2)

Solution:

Step 1: Factor: (x - 2)(x + 2) < 0. Step 2: Test intervals: solution is (-2, 2).

What is the solution set for the inequality: x^2 - 4 < 0?

What is the solution set for the inequality: x^2 - 4 < 0?

Step 1: Start with the inequality x^2 - 4 < 0.
Step 2: Factor the left side: x^2 - 4 can be factored into (x - 2)(x + 2).
Step 3: Rewrite the inequality: (x - 2)(x + 2) < 0.
Step 4: Identify the critical points by setting each factor to zero: x - 2 = 0 gives x = 2, and x + 2 = 0 gives x = -2.
Step 5: These critical points divide the number line into intervals: (-∞, -2), (-2, 2), and (2, ∞).
Step 6: Test a point from each interval to see where the product (x - 2)(x + 2) is negative.
Step 7: For the interval (-∞, -2), test x = -3: (-3 - 2)(-3 + 2) = (-5)(-1) = 5 (not negative).
Step 8: For the interval (-2, 2), test x = 0: (0 - 2)(0 + 2) = (-2)(2) = -4 (negative).
Step 9: For the interval (2, ∞), test x = 3: (3 - 2)(3 + 2) = (1)(5) = 5 (not negative).
Step 10: The solution set where the product is negative is the interval (-2, 2).

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