Set 8: Linear Inequalities (Advanced)

Explanation

Answer: A

Solve: $|x - 3| < 5$

$-2 < x < 8$

✓ Correct

$x < 8$

$x < -2$ or $x > 8$

$-8 < x < 2$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Absolute value inequalities with $<$ become compound "and" inequalities. 1. Setup: $-5 < x - 3 < 5$ 2. Add 3: $-5 + 3 < x < 5 + 3$ 3. Simplify: $-2 < x < 8$ Strategic Tip: $|A| < b$ becomes $-b < A < b$ . Think "Less thAND" (Less than = And). Choice B is incorrect because it ignores the lower bound. Choice C is incorrect because it models $|x-3| > 5$ ("GreatOR" = Or). Choice D is incorrect because it solves incorrectly.

Key Steps:

•

The correct answer is $-2 < x < 8$

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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