Question

In short terms, how would you folks describe an absolute value inequality?

Answer 1

`|x-a| < 2`

the distance between `x` and `a` must be less than `2`

Answer 2

Notice that `|x-a|` represents the distance between x and a on number line

Answer 3

You could start by describing y=|x|. You could draw its graph. You could explain what this function does to x if x happens to be positive or zero. you could explain what this function does to x if x happens to be negative.

Answer 4

For example, to provide a definition. Thank you again.

Answer 5

I like rational's explanations.

I asked you to graph y=|x|. According to rational, |x-a| represents the distance from the point x on the number line to some other point 'a' on the number line. Did you realize that y=|x| and y=|x-0| are the same? This means that |x| represents the distance of x from the origin.

sorry, dumbsearch, but I don't give out "answers to order." I'll give you the basic hamburger, with several solid examples, as has done rational. Now it's up to you to take this info and run with it. Let's see your draft of an explanation of the "an absolute value equation."

Then you could modify that slightly to describe "an absolute value inequality."

Answer 6

I'm not asking you to; I just don't entirely understand the concept.
Though thank you, I will read through what you provided to me.

Answer 7

rational's "|x-a| < 2" is just that: an absolute value inequality. Based on the info he and I have given you, write something, even the most basic something, to demonstrate your beginning understanding of this concept. We'd then be happy to give you feedback on your attempt.

Answer 8

Thank you.

Answer 9

You're very welcome. Sorry for being a bit caustic. Hope this helps you get started. Actually, I do intend to stick around for a few minutes longer, in case you do write something and want my feedback on it.

Answer 10

I understand, you are a retired math professor, haha, and you have to deal with stupid students like me :p

Answer 11

Thank you though, the information provided did help. It's nice that you offer to help me further if I need to.

Answer 12

Believe me, I never thought, or said, that you were 'stupid.' Thanks for checking out my background. In my old age I twist a few arms, but still try to be supportive of those who really want to learn the subject matter. Best to you. mathmale.

Answer 13

I never said that you said I am stupid, just recognizing that its nice that you help people beneath your skill level, and I understand why you would be a little bit "caustic".

Answer 14

Thanks! Great to be on the same wavelength with you.

Answer 15

Thank YOU! You're the one helping, haha.

Answer 16

I just reread what you wrote, and you said:
> Let's see your draft of an explanation of the "an absolute value equation."

Here's what I wrote for an absolute value equation earlier:

An absolute value equation is almost the same as a linear equation, expect that the variables are within an absolute value symbol. As a result, there are two different equations, one where the the contents within the absolute value symbol are positive, and another where they are negative. When a absolute value equation is graphed, it is on a coordinate plane and its geometrical figure is a line. However, they are two different lines that are graphed due to the two different results. There is no shading on the graph. In this particular example, I am using | x + 2 | = 7 as an absolute value equation. I will proceed to solve it as a regular linear equation, while splitting and calculating it into two different forms, both (x + 2) = 7 and –(x + 2) = 7. The solution for the first one is x = –9, and the second solution is x = 5. To confirm this graphically, you would look for the intersections of y1 = | x + 2 | and y2 = 7.

Answer 17

Have any idea how I can modify it to work with the absolute value inequality?

Answer 18

Any ideas? @mathmale

Answer 19

I'm reading your draft now!

Answer 20

Thank you :)

Answer 21

Typing out some suggestions for you. Not done yet. See the attached.

Answer 22

Again I have overlooked the fact that we're discussing abs. val. inequalities. But you can change the wording around a bit to reflect that.

Answer 23

See the latest attachment. I'm afraid I'm going to have to stop here and now, but hope that the suggestions I'm giving you here prove to be helpful, both in your understanding of the absolute value function and abs. val. inequalities.

Answer 24

Thank you! :)

Answer 25

I am very grateful for all the help you have provided. Seriously, I wish all professors were as nice as you!

Answer 26

:)