This Blog exists for the collective benefit of ALL Algebra students. While the posts are usually specific to Mr. Chamberlain's class, any and all "algebra-ticians" are welcome. The more specific your question (including your own attempts to answer it) the better.

Thursday, November 17, 2016

hw #3-6B OO-FAH! AGAIN!!

hw #3-6B OO-FAH! AGAIN!! Due Mon 11/21(A)/Tues 11/22(B)

For #11 in 3-6 of the packet, I got 3y <= 4y-2 <=26. I do not see any visible mistakes in my work, so I am assuming that is the answer. If it is the answer, how would I graph it? I cannot do anything else to simplify, so would I keep the 3y and 4y-2?

A VERY SHINY, LUMINESCENT QUESTION, INDEED!!!!! I hope that everyone thanks you for asking. You are about to learn that Humpty-Dumpty is alive and well and helping you solve compound inequalities!!

We need to remember that COMPOUND inequalities are just that, MULTIPLE INDIVIDUAL INEQUALITIES COMBINED.

As I think you know by now, we ALWAYS work on the "OR" inequalities (aka OO-FAHs) separately. When solving AND inequalities (aka TWEENERS), we sometimes do the "Boston Market Shuffle" and work on all three sides at the same time. However, there are some cases where this technique doesn't work, and you just have to work them two sides at a time. :(... this sadly, is one of those times.

In this case, the original problem was: 4 <= y + 2 <= -3(y - 2) + 24

I can see that you simplified the right side and then added 3y to all three sides... hmmm... no matter how hard you try, you seem to have "y" on two out of three sides, right? ARGH... then you are STUCK!! The good news is, since you used POIs (Props of Inequality) you're still in balance.

Here's what you have to do... SPLIT the three-sider into TWO two-siders, like this:

Inequality #1 3y <= 4y - 2

Inequality #2 4y - 2 <= 26

You can solve these inequalities SEPARATELY and then simply take your two separate answers (connected with an AND) and graph them and write them as a "tweener."

Essentially, this is what happened. Humpty-Dumpty (the compound inequality) fell off the wall, split into two inequalities which we solved one at a time, and then put back together again as a very happy TWEENER!!

This is what developing our math skills is all about... learning how to recognize when it is appropriate to CHUNK problems into smaller manageable pieces that we can solve with our prior knowledge, whether it is what we learned from Mr. & Ms. McG back in 4th and 5th grade (i.e. the simple math we could apply to positive and negative integers), or what we learned two weeks ago when we learned how to work with inequalities.

If a compound inequality has an 'or' in it, how would we do a 3-way check. Would we put an 'or' for the Want = and have two different checks? For example, a 3 or 4 based on what would be equal for both inequalities?

I think I'll say yup... if you wanted to be totally thorough, you could actually do a "5-way" check!! You should check your "border" values and values that are in between the border values AND to the left or right of the border values.

Let's say had an OO-FAH ("OR" inequality) such as:

2x < -8 OR 3x >= 21

... that "obviously" solves to the following:

X = { x | x<-4 or x>=7}

At a minimum, you should check for x = -4 in the original "2x < -8" inequality and check for x = 7 in the original "3x >= 21" inequality. Then, you would want to check for any number in between -4 and 7 to see that it made both of those inequalities FALSE.

In the final analysis, you should only check your answers on problems that you want to get right!!

For #11 in 3-6 of the packet, I got 3y <= 4y-2 <=26. I do not see any visible mistakes in my work, so I am assuming that is the answer. If it is the answer, how would I graph it? I cannot do anything else to simplify, so would I keep the 3y and 4y-2?

ReplyDeleteDear Sparkle,

DeleteA VERY SHINY, LUMINESCENT QUESTION, INDEED!!!!! I hope that everyone thanks you for asking. You are about to learn that Humpty-Dumpty is alive and well and helping you solve compound inequalities!!

We need to remember that COMPOUND inequalities are just that, MULTIPLE INDIVIDUAL INEQUALITIES COMBINED.

As I think you know by now, we ALWAYS work on the "OR" inequalities (aka OO-FAHs) separately. When solving AND inequalities (aka TWEENERS), we sometimes do the "Boston Market Shuffle" and work on all three sides at the same time. However, there are some cases where this technique doesn't work, and you just have to work them two sides at a time. :(... this sadly, is one of those times.

In this case, the original problem was:

4 <= y + 2 <= -3(y - 2) + 24

I can see that you simplified the right side and then added 3y to all three sides... hmmm... no matter how hard you try, you seem to have "y" on two out of three sides, right? ARGH... then you are STUCK!! The good news is, since you used POIs (Props of Inequality) you're still in balance.

Here's what you have to do...

SPLIT the three-sider into TWO two-siders, like this:

Inequality #1

3y <= 4y - 2

Inequality #2

4y - 2 <= 26

You can solve these inequalities SEPARATELY and then simply take your two separate answers (connected with an AND) and graph them and write them as a "tweener."

Essentially, this is what happened. Humpty-Dumpty (the compound inequality) fell off the wall, split into two inequalities which we solved one at a time, and then put back together again as a very happy TWEENER!!

This is what developing our math skills is all about... learning how to recognize when it is appropriate to CHUNK problems into smaller manageable pieces that we can solve with our prior knowledge, whether it is what we learned from Mr. & Ms. McG back in 4th and 5th grade (i.e. the simple math we could apply to positive and negative integers), or what we learned two weeks ago when we learned how to work with inequalities.

Blog on, Sparkle!

Thank you for asking.

Deleteበመጠየቅ እናመሰግናለን.

Dankie dat jy vra.

Faleminderit që Pyete.

شكرا لسؤالك.

Well, I guess we'll count that as thanks from just about EVERYONE!

Deletedzięki (polish)

If a compound inequality has an 'or' in it, how would we do a 3-way check. Would we put an 'or' for the Want = and have two different checks? For example, a 3 or 4 based on what would be equal for both inequalities?

ReplyDeleteI think I'll say yup... if you wanted to be totally thorough, you could actually do a "5-way" check!! You should check your "border" values and values that are in between the border values AND to the left or right of the border values.

DeleteLet's say had an OO-FAH ("OR" inequality) such as:

2x < -8 OR 3x >= 21

... that "obviously" solves to the following:

X = { x | x<-4 or x>=7}

At a minimum, you should check for x = -4 in the original "2x < -8" inequality and check for x = 7 in the original "3x >= 21" inequality. Then, you would want to check for any number in between -4 and 7 to see that it made both of those inequalities FALSE.

In the final analysis, you should only check your answers on problems that you want to get right!!