Set 17: Linear Inequalities

Explanation

Answer: A

A shipping container must weigh more than 1000 lbs but less than 5000 lbs. Which inequality represents the weight $w$ ?

$1000 < w < 5000$

✓ Correct

$1000 \leq w \leq 5000$

$w > 1000$ or $w < 5000$

$w < 1000$ or $w > 5000$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. "More than" and "Less than" are strict inequalities. 1. Lower: $w > 1000$ 2. Upper: $w < 5000$ 3. Compound: $1000< w < 5000$ Strategic Tip: "Between" usually implies an intersection (AND), written as a single chain. Choice B is incorrect because it includes the weights 1000 and 5000. Choice C is incorrect because "or" would make this true for ALL numbers (since any number is either $>1000$ or $<5000$ ). Choice D is incorrect because it represents the weights OUTSIDE the allowed range.

Key Steps:

•

The correct answer is $1000< w < 5000$

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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Set 17: Linear Inequalities

Detailed Explanation

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