Question

The weather forecast for Fairbanks, Alaska, warned listerneres that the daytime high temperature of 2 degrees below zero wouuld drop to a nighttime lowof 28 degrees below. By how many degrees did the temperature fall overnight?

Answer 1

Option 1: assuming value of variable \(x\) is negative;
use the equation\[-2+x=-28\]from this we resolve with \(x=-28-(-2)=-28+2=-26\)
As a result, your answer would be \(-26\) degrees fallen overnight.

Option 2: assuming value of variable \(x\) is absolute-value;
use the equation \[-2-x=-28\]from this we resolve with \(-x=-28-(-2)=-28+2=-26\)
However, there is an extra step here to fully isolate the variable. To do so, we must divide both sides by negative 1:\[-x\div-1=-26\div-1\]Result should now be \(x=26\).

Here presents an issue: both results are logically correct by context. However, the person who asked me about this dilemma did option one, while their professor used option two. In this scenario, which option should be favored for the sake of studying/exams?

Answer 2

This is a somewhat a semantic issue, but I would argue that the verb "fall" implies you would use a positive result. You say "the temperature fell 26 degrees" not "the temperature fell -26 degrees"

Answer 3

I forgot to add that I already know how to do this, it's more of a "which is better" situation. Ultimately both mean the same thing - the temperature fell 26 degrees - but since the professor uses ONLINE testing this is a point of contention for the student who came to me for help.

Answer 4

erk - that posted too late :\

Answer 5

that being said, if they ask "what is the net change in temperature" i would opt for the negative result

Answer 6

I mean, my reply posted too late. I blame lag.

Also, rewording my typo-ridden post:
The weather forecast for Fairbanks, Alaska, warned listeners that the daytime high temperature of 2 degrees below zero would drop to a nighttime low of 28 degrees below. By how many degrees did the temperature fall overnight?

Answer 7

Oh okay. So basically assume \(x\) takes on an absolute-value context?
(It's past midnight so pardon me if that makes zero sense. But I get what you mean)

Answer 8

in this case yes, because of the word "fall" I would not assume a sign for x

Answer 9

OH. I think I get it. Because the query sentence used the word "fall" as well, there is no signage?

Answer 10

...mathematical grammar is weird. And I'm STEM.

Answer 11

yeah

Answer 12

Thanks! I'll keep this up as a tutorial/advice thread for everyone else if that's okay?

(I would edit the post but it's bugged lol)

Answer 13

I don't know about that, I'll ask the other mods and see what they think

Answer 14

oh sometimes I write a couple of maths posts and keep them up for a few weeks lol
To assist people who struggle with word problems

Answer 15

Oh, I just realized a simplified way to read it: "How much integers did -2 go down to reach -28?"

Or something like that. I got drawn into a debate on maths language, great.

Answer 16

In real life.
But anyway, I thought I could answer a couple of word problems for the sake of helping those who don't compute mathematical language that easily