2

Set 7: Linear Inequalities

Explanation

Answer: A

A refrigerator temperature must be kept between 34°F and 40°F, inclusive. Which inequality represents an ALARM condition (temperature is unsafe)?

A.

t<34t < 34 or t>40t > 40

✓ Correct
B.

34t4034 \leq t \leq 40

C.

t34t \leq 34 or t40t \geq 40

D.

34<t<4034 < t < 40

Detailed Explanation

Choice A is correct. Choice A is the correct answer. The alarm sounds when the temperature is OUTSIDE the safe range. 1. Safe Range: 34t4034\leq t \leq 40 (inclusive) 2. Unsafe (Alarm): strictly less than 34 OR strictly greater than 40 3. Inequality: t<34t < 34 or t>40t > 40 Strategic Tip: The negation of "between inclusive" is "outside exclusive". Choice B is incorrect because it represents the SAFE range. Choice C is incorrect because it includes the boundary values 34 and 40 as unsafe, but the problem says "inclusive" is safe. Choice D is incorrect because it represents a strictly safe range, excluding boundaries.

Key Steps:

The correct answer is t<34t < 34 or t>40t > 40

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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