Given:
Checked bags must weigh 40 lb or less, or passengers will have to pay a fee for an oversized bag.
To Find:
An inequality that represents the weight of a checked bag that will not result in a fee and any solutions to the inequality that do not make sense for this situation.
Answer:
w ≤ 40 is the inequality representing the weight of a checked bag that will not result in a fee.
The only solutions to this inequality that may not make sense are if the weight of the bag is less than 0 lb (which is not possible) or even weighing exactly 0 lb (which is possible, but not practical).
Explanation:
Let w denote the weight of the bag, as per the question.
Given that checked bags have to weigh 40lb or less, we have
w ≤ 40
that is, any checked bag has to weigh less than 40lb or 40lb exactly, to avoid paying the fee.
So, w ≤ 40 is the inequality representing the weight of a checked bag that will not result in a fee.
The only solutions to this inequality that may not make sense are if the weight of the bag is less than 0lb (i.e., in negative) as weight is a physical quantity that can only take positive values. Practically speaking, any checked bag will also not weigh exactly 0lb so, we can modify the above inequality to write
0 < w ≤ 40