5
algebra

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

A

No solution

B

All real numbers

C

x<1x < -1

D

1<x<1-1 < x < 1

Correct Answer: A

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.