6
algebra

Which inequality has all real numbers as solutions?

A

3x+5>3x23x + 5 > 3x - 2

B

2x7<2x+12x - 7 < 2x + 1

C

x+4x+4x + 4 \geq x + 4

D

All of the above

Correct Answer: D

Choice D is the correct answer. Each inequality simplifies to a true statement.

  1. Choice A: Subtract 3x3x: 5>25 > -2 ??(always true)
  2. Choice B: Subtract 2x2x: 7<1-7 < 1 ??(always true)
  3. Choice C: Subtract xx: 444 \geq 4 ??(always true)
  4. All three are identities (true for all xx)

?�� Strategic Tip: When variables cancel and leave a true statement, all real numbers satisfy the inequality.

Choices A, B, and C individually are incomplete because all three inequalities have all real numbers as solutions.