4
algebra

A temperature sensor displays valid readings between -10°C and 50°C, inclusive. Which inequality represents valid temperature TT?

A

−10<T<50-10 < T < 50

B

−10≤T≤50-10 \leq T \leq 50

C

T<−10T < -10 or T>50T > 50

D

T≥−10T \geq -10 and T≥50T \geq 50

Correct Answer: B

Choice B is the correct answer. Compound inequalities with "and" represent ranges between two values.

  1. Lower bound: "At least -10" means T≥−10T \geq -10
  2. Upper bound: "At most 50" means T≤50T \leq 50
  3. Combine: −10≤T≤50-10 \leq T \leq 50 (both conditions simultaneously)
  4. Note: "Inclusive" requires ≤\leq and ≥\geq, not strict inequalities

?�� Strategic Tip: "Between X and Y, inclusive" always uses ≤\leq on both sides: X≤var≤YX \leq \text{var} \leq Y.

Choice A is incorrect because it uses strict inequalities, excluding the boundary values -10 and 50. Choice C is incorrect because it represents temperatures OUTSIDE the valid range using "or" logic. Choice D is incorrect becauseT≥−10T \geq -10 and T≥50T \geq 50 would mean T≥50T \geq 50 only (impossible to satisfy both with "and" as written).

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Linear Functions Set 63