extreme value operations--one extreme value minus (-) anothe

[wignewton]

On page 92 of the 3rd edition Equations, Inequalities, and VICS there is a chart listing legal operations on extreme values. What if I need to subtract one extreme value from another extreme value and not from a number ie. GT-2 - LT12? What does the extreme value become then? Also, question on strategy: What if you are given a question like this: If 3<b<16 and -1<a<23, which of the following CANNOT be true? Then a list of 4 options are given(I have not used the true numbers, as this is a problem from another text, ie copyright problems), would you approach this with the extreme values approach or would you use another approach? Thanks!

[esledge]

What if I need to subtract one extreme value from another extreme value and not from a number ie. GT-2 - LT12? What does the extreme value become then?

In that case, you have to think about how the GT's or LT's compound. Let's look at your example, GT(-2) - LT(12).

I first do the math with the numbers alone: -2-12 = -14.

Then, I look at whether it's exactly -14, LT(-14), or GT(-14). For that, I do the "math" with the abbreviations: GT - LT = more - less = more = GT.

To give a few more examples:

GT(-2) - LT(12) --> more - less = more --> GT(-14)
LT(-2) - GT(12) --> less - more = less --> LT(-14)
GT(-2) + GT(12) --> more + more = more --> GT(10)
LT(-2) + LT(12) --> less + less = less --> LT(10)

Watch out! You shouldn't approach problems this way when you see cases like this:
GT(-2) - GT(12) --> more - more = it depends on how MUCH more...
LT(-2) - LT(12) --> less - less = it depends on how MUCH less...
GT(-2) + LT(12) --> more + less = it depends on how MUCH more/less...
LT(-2) + GT(12) --> less + more = it depends on how MUCH more/less...

Also, question on strategy: What if you are given a question like this: If 3<b<16 and -1<a<23, which of the following CANNOT be true?

It depends. If the answers had (a+b) in them, I would line up the signs facing the same way and add the inequalities:

3 < b < 16
+(-1 < a < 23)
2 < a + b < 39

If the answers had (a-b) in them, I would rephrase that as a-b = a+ (-b), then turn 3<b<16 into -3>-b>-16 (by multiplying the whole thing by -1, remembering to flip the signs). Then I'd add the inequalities for a and for -b, remembering to line up the signs facing the same way:

-1 < a < 23
+(-16 < -b < -3)
-17 < a - b < 20

If the answers had ab in them, I would think about the possible products of the extremes, first from a sign perspective. a can be neg, zero, or positive. b can be only positive. Therefore the product ab can be neg, zero, or positive. What's the negative limit? The more negative of (-1)(3) or (-1)(16). It's -16. What's the positive limit? The more positive of (23)(3) or (23)(16). It's 368. Therefore, -16<ab<368.

[heel2891]

Can you give more examples of extreme value operations such as cases of division and multiplication of one extreme value by a regular number (both positive and negative) when the extreme values are attached to both positive and negative numbers.

I know that -7xLT2=GT(-14) but what about 7xLT-2? Or what about 7xGT-2?

I know that 8/LT2 =G4 if LT2 is positive but what if LT2 is negative or what if it is -8/LT2 or -8/LT-2? What if it is LT2/8 is it GT 1/4?

And to multiply two extreme values together when that are not both positive like GT-8 x GT8 or GT-8 x GT-8 or LT-8 x LT-8

What about dividing two extreme values under different positive and negative combinations?

I guess I'm asking if you can lay out all the different possibilities for extreme value operations because page 92 of the Equations, Inequalities, VICS guide 4th edition only lays out sample operations but I have encountered many scenarios other than those examples and couldn't proceed with confidence so that strategy was basically rendered useless and cost me lots of time.

So when should I feel free to use extreme value shortcuts and when should I not?

Thanks for any guidance you may provide on this...

[jnelson0612]

Can you give more examples of extreme value operations such as cases of division and multiplication of one extreme value by a regular number (both positive and negative) when the extreme values are attached to both positive and negative numbers.

I know that -7xLT2=GT(-14) but what about 7xLT-2? Or what about 7xGT-2?

I know that 8/LT2 =G4 if LT2 is positive but what if LT2 is negative or what if it is -8/LT2 or -8/LT-2? What if it is LT2/8 is it GT 1/4?

And to multiply two extreme values together when that are not both positive like GT-8 x GT8 or GT-8 x GT-8 or LT-8 x LT-8

What about dividing two extreme values under different positive and negative combinations?

I guess I'm asking if you can lay out all the different possibilities for extreme value operations because page 92 of the Equations, Inequalities, VICS guide 4th edition only lays out sample operations but I have encountered many scenarios other than those examples and couldn't proceed with confidence so that strategy was basically rendered useless and cost me lots of time.

So when should I feel free to use extreme value shortcuts and when should I not?

Thanks for any guidance you may provide on this...

Hey heel,
Laying out all the possibilities is probably beyond the scope of this forum. May I suggest that you pick some numbers and start doing exactly what you are asking? Calculate some of these values out and notice what happens. You will learn much more thoroughly than if we just tell you, and if you like you can report back what happens in these scenarios.

I think that once you lay out the scenarios you will get a better sense of when these strategies are appropriate to use and when they are not. However, once you do these calculations please come back and let's discuss if you are still struggling in this area.