7
algebra

Which compound inequality has NO solution?

A

x<3x < 3 and x>5x > 5

B

x<3x < 3 or x>5x > 5

C

x>3x > 3 and x<5x < 5

D

x>3x > 3 or x<5x < 5

Correct Answer: A

Choice A is the correct answer. Analyze the logic of "and".

  1. Condition: A number must be less than 3 AND greater than 5 simultaneously.
  2. Logic: No number exists that satisfies both. The sets are disjoint.
  3. Result: Empty set (No solution).

?�� Strategic Tip: "And" requires overlap. If the arrows point away from each other with a gap, there is no overlap.

Choice B is incorrect because "Or" allows disjoint sets (this is a valid inequality). Choice C is incorrect because numbers like 4 satisfy this (3<x<53 < x < 5). Choice D is incorrect because this covers all real numbers (overlapping rays).