6
algebra

Which inequality corresponds to the statement: "Three times a number minus 5 is at most 4 more than twice the number"?

A

3x52x+43x - 5 \leq 2x + 4

B

3x5<2x+43x - 5 < 2x + 4

C

3(x5)2x+43(x - 5) \leq 2x + 4

D

3x52x+43x - 5 \geq 2x + 4

Correct Answer: A

Choice A is the correct answer. Translate the sentence phrase by phrase.

  1. "Three times a number minus 5": 3x53x - 5
  2. "Is at most": \leq
  3. "4 more than twice the number": 2x+42x + 4
  4. Combine: 3x52x+43x - 5 \leq 2x + 4

?�� Strategic Tip: "At most" means less than or equal to (\leq). "More than" in "4 more than..." means addition (+4+4).

Choice B is incorrect because "at most" includes equality, so << is wrong. Choice C is incorrect because it groups (x5)(x-5), implying "Three times the difference of a number and 5". Choice D is incorrect because\geq means "at least", not "at most".