10
algebra

A concert ticket costs at least $45 but no more than $120. Which compound inequality represents the ticket price pp?

A

45<p<12045 < p < 120

B

45≤p≤12045 \leq p \leq 120

C

p≤45p \leq 45 or p≥120p \geq 120

D

p<45p < 45 or p>120p > 120

Correct Answer: B

Choice B is the correct answer. Translating "at least" and "no more than" requires proper inequality symbols.

  1. Lower bound: "At least $45" means p≥45p \geq 45 (includes 45)
  2. Upper bound: "No more than $120" means p≤120p \leq 120 (includes 120)
  3. Combine: 45≤p≤12045 \leq p \leq 120 (both conditions with "and")

?�� Strategic Tip: "At least" = ≥\geq (minimum), "at most"/"no more than" = ≤\leq (maximum).

Choice A is incorrect because it uses strict inequalities, excluding the boundary prices $45 and $120. Choice C is incorrect because it represents prices OUTSIDE the range using "or" logic, the opposite of what we want. Choice D is incorrect because it combines strict inequalities with "or", representing all prices except the range 45-120.

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Linear Functions Set 63