Which of the following is a solution of the inequality

[JeffM]

You're right!. I have to look at the answer choices. Sometimes you can tell by just looking at them. Not many times, but this one here is an example
Thanks!

Not quite.

If you had not found out that - 2 < x < 2, you would have had to test all four answers against the less intuitively obvious
- 3 < 2x+ 1 < 5. The preliminary work of simplifying to - 2 < x < 2 lets your intuition "see" the "obvious" answer. Simplification is something that works with your intuition. I think that if you say "Let my intuition have a go" before you do any simplification, you will waste time on balance.

 

[eddy2017]

Not quite.

If you had not found out that - 2 < x < 2, you would have had to test all four answers against the less intuitively obvious
- 3 < 2x+ 1 < 5. The preliminary work of simplifying to - 2 < x < x lets your intuition "see" the "obvious" answer. Simplification is something that works with your intuition. I think that if you say "Let my intuition have a go" before you do any simplification, you will waste time on balance.

That is right too. It looked way easier after simplification.

 

[Steven G]

Not quite.

If you had not found out that - 2 < x < 2, you would have had to test all four answers against the less intuitively obvious
- 3 < 2x+ 1 < 5. The preliminary work of simplifying to - 2 < x < 2 lets your intuition "see" the "obvious" answer. Simplification is something that works with your intuition. I think that if you say "Let my intuition have a go" before you do any simplification, you will waste time on balance.

I 2nd JeffM's response.
You will have to check up to 4 choices working backwards.
Solving the inequality for x was just one step. Then picking the choice that has a number between -2 and 2 should be effortless.

 

[eddy2017]

I 2nd JeffM's response.
You will have to check up to 4 choices working backwards.
Solving the inequality for x was just one step. Then picking the choice that has a number between -2 and 2 should be effortless.

Yes, once I solve the inequality the number to choose was child's play. It like JeffM says: It would not save any time at going thru the values for x . If anything it would used up same amount of time.

Thanks, Steven and Jeff.

 

[Steven G]

Yes, once I solve the inequality the number to choose was child's play. It like JeffM says: It would not save any time at going thru the values for x . If anything it would used up same amount of time.

Either you are totally confused or I am totally confused.
In your first post you did solve the inequality. This is not negotiable, you did solve it.
Having solved the inequality you made this post because you did not know which choice to pick.
Now you say after solving the inequality, knowing which choice to pick is child's play.
Well, which is it? Is it child's play or is it unclear to you which choice to pick.
If I were you I would try to say as little as possible as you get caught up in almost everything that you say.

 

[Deleted member 4993]

Either you are totally confused or I am totally confused.
In your first post you did solve the inequality. This is not negotiable, you did solve it.
Having solved the inequality you made this post because you did not know which choice to pick.
Now you say after solving the inequality, knowing which choice to pick is child's play.
Well, which is it? Is it child's play or is it unclear to you which choice to pick.
If I were you I would try to say as little as possible as you get caught up in almost everything that you say.

Steven,

You are correct but I think this topic should be discussed with a PM.

 

[eddy2017]

Steven,

You are correct but I think this topic should be discussed with a PM.

No, Steve as much as it pains me to say you're not correct. You have misunderstood me. I said that anyone with good math skills could have figured out the value for x without solving the inequalites. And tutors have agreed with me even if they know that solving the inequality makes it easier and perhaps quicker.
Jeff didn't have to solve it to know you either pka either Bbb either and so forth do on. That was the whole point of what we have been discussing. I'm sorry

 

[JeffM]

@eddy2017

Let's take this one step at a time.

You succeeded in simplifying the inequality on your own. Your mathematical mechanics were fine. This did not help you find the answer because you did not understand what the question was asking. Nor would working backwards necessarily have helped you when you were unsure of what you were looking for. So let's clear up that confusion before we proceed. When you "solve" an equation, you hope to get a single numeric answer or at least a small number of numeric answers. When you "solve" an inequality, you get a range of numbers. This is the general idea behind this problem: it was asking you to find which of the given numbers was in the designated range to make clear that you will almost never get a unique answer from an inequality. That is what you should take mathematically from this problem.

Almost always, you can solve multiple choice problems in algebra by working backward from the proposed answers to see what makes the initial problem true. If you have five proposed answers, it will on average take at least double the time to work backward as to solve the problem directly. And with practice problems, you will not learn whatever lesson the exercise is trying to teach. I view it as a desperation move (not that I have not done it when I was desperate). But you should not view it as a starting point.

Sometimes, you do not have to solve the problem completely to know which multiple choice answer is correct. In this specific case, simplification would allow you to "see" which answer is correct if you understand exactly what question is being asked. I think there are two practical lessons to be learned here. One is that simplification is almost always where you should start: things may become obvious as soon as simplification is complete. Second is that when you get stuck, reread the question with care. Here you initially missed a clue in the use of "a" rather than "the."

 

[eddy2017]

@eddy2017

Let's take this one step at a time.

You succeeded in simplifying the inequality on your own. Your mathematical mechanics were fine. This did not help you find the answer because you did not understand what the question was asking. Nor would working backwards necessarily have helped you when you were unsure of what you were looking for. So let's clear up that confusion before we proceed. When you "solve" an equation, you hope to get a single numeric answer or at least a small number of numeric answers. When you "solve" an inequality, you get a range of numbers. This is the general idea behind this problem: it was asking you to find which of the given numbers was in the designated range to make clear that you will almost never get a unique answer from an inequality. That is what you should take mathematically from this problem.

Almost always, you can solve multiple choice problems in algebra by working backward from the proposed answers to see what makes the initial problem true. If you have five proposed answers, it will on average take at least double the time to work backward as to solve the problem directly. And with practice problems, you will not learn whatever lesson the exercise is trying to teach. I view it as a desperation move (not that I have not done it when I was desperate). But you should not view it as a starting point.

Sometimes, you do not have to solve the problem completely to know which multiple choice answer is correct. In this specific case, simplification would allow you to "see" which answer is correct if you understand exactly what question is being asked. I think there are two practical lessons to be learned here. One is that simplification is almost always where you should start: things may become obvious as soon as simplification is complete. Second is that when you get stuck, reread the question with care. Here you initially missed a clue in the use of "a" rather than "the."

Thank you, Jeff. It was not only helpful but on point. I thought I could get only a number when I solved it hence my confusion when I look at the number choices. You knew right away why and where I was confused. Thank you.
One question: Even if it takes more time trying all values for x
It is , by the way, a very simple inequality).
Could you solve that just by looking at the answer choice?.
I'm not talking about method I'm talking about skills. Could you have done it?

 

[JeffM]

Thank you, Jeff. It was not only helpful but on point. I thought I could get only a number when I solved it hence my confusion when I look at the number choices. You knew right away why and where I was confused. Thank you.
One question: Even if it takes more time trying all values for x
It is , by the way, a very simple inequality).
Could you solve that just by looking at the answer choice?.
I'm not talking about method I'm talking about skills. Could you have done it?

I am not sure what you mean

If you mean, could I have "seen" the correct answer just by looking at the initial inequality and looking at the choices for the answer? Possibly because, as you say, it is not a very complex inequality. But probably not because 2 and - 2 are so close to being in the range. They in fact represent the end points of the open interval that does contain the valid answers. In other words, it is a subtle enough question that MY intuition would probably not have solved it.

If on the other hand, you mean would I have tried to solve it by inspection, the answer is definitely not. Why? Because I know that inequalities usually represent a range and that there can be subtleties in specifying that range exactly. So I would have proceeded exactly as you did, namely to find the exact range.

In my opinion, you are barking up the wrong tree here. The lessons to learn here are: inequalities almost always specify a range, simplify from the start, and make sure you understand what the problem is asking. Someone with fabulous intuition and experience may be able to solve a lot of problems by simple inspection, but normal people like me do not have that level of intuition.

 

[eddy2017]

I am not sure what you mean

If you mean, could I have "seen" the correct answer just by looking at the initial inequality and looking at the choices for the answer? Possibly because, as you say, it is not a very complex inequality. But probably not because 2 and - 2 are so close to being in the range. They in fact represent the end points of the open interval that does contain the valid answers. In other words, it is a subtle enough question that MY intuition would probably not have solved it.

If on the other hand, you mean would I have tried to solve it by inspection, the answer is definitely not. Why? Because I know that inequalities usually represent a range and that there can be subtleties in specifying that range exactly. So I would have proceeded exactly as you did, namely to find the exact range.

In my opinion, you are barking up the wrong tree here. The lessons to learn here are: inequalities almost always specify a range, simplify from the start, and make sure you understand what the problem is asking. Someone with fabulous intuition and experience may be able to solve a lot of problems by simple inspection, but normal people like me do not have that level of intuition.

Okay, good. Totally got it. Thanks.

 

[Steven G]

Thank you, Jeff. It was not only helpful but on point. I thought I could get only a number when I solved it hence my confusion when I look at the number choices. You knew right away why and where I was confused. Thank you.
One question: Even if it takes more time trying all values for x
It is , by the way, a very simple inequality).
Could you solve that just by looking at the answer choice?.
I'm not talking about method I'm talking about skills. Could you have done it?

Eddy,
You said that once you solved the inequality that the rest was child's play. Now you say I thought I could get only a number when I solved it hence my confusion when I look at the number choices.
I must say that you are amazing.

 

[eddy2017]

Eddy,
You said that once you solved the inequality that the rest was child's play. Now you say I thought I could get only a number when I solved it hence my confusion when I look at the number choices.
I must say that you are amazing.

Steven, it was all confusion on my part,
and maybe I got too wordy, like you said,
I know what you meant though.
And the good thing is that I learned one thing out of this exercise: solving an inequality does not necessarily have to give me one single value. It can give me a simplified inequality with a range. That was very interesting.
Thank you for your input and help. I always appreciate you no end.

 

[Steven G]

The most simply inequality, like x<4, gives many values for x. That is what inequalities is all about.

 

[eddy2017]

The most simply inequality, like x<4, gives many values for x. That is what inequalities is all about.

Thanks.