6

Set 9: Linear Inequalities

Explanation

Answer: A

Solve: 3x+5<23|x| + 5 < 2

A.

No solution

✓ Correct
B.

All real numbers

C.

x<1x < -1

D.

1<x<1-1 < x < 1

Detailed Explanation

Choice A is correct. Choice A is the correct answer. Isolate the absolute value. 1. Subtract 5: 3x<33|x| < -3 2. Divide by 3: x<1|x| < -1 3. Logic: Absolute value cannot be less than a negative number. Strategic Tip: Stop as soon as you see ...<negative|...| < \text{negative}. Choice B is incorrect because it is never true. Choice C is incorrect because it implies solutions exist. Choice D is incorrect because it implies solutions exist.

Key Steps:

The correct answer is No solution

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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