How to represent this absolute value inequality with constants?

[kenny1999]

Homework Statement

absolute value

Relevant Equations

inequality

see attached image, it asks to repesent it in x-graph
constant "a" isn't conditioned.
Do I need to separate it into a few cases of the constant a and represent each in one x-graph?

 

[PeroK]

What do you mean by an x-graph? Do you mean on the x-axis?

 

[anuttarasammyak]

You should read that the formula means x is around a within distance $\epsilon$.

 

[kenny1999]

What do you mean by an x-graph? Do you mean on the x-axis?

yes. Sorry I am not in English language

 

[kenny1999]

You should read that the formula means x is around a within distance $\epsilon$.

a isn't conditioned, e.g. >0 or <0

so do I need to separate into a few cases and draw the graph??

 

[kenny1999]

OK . This is what I have done, I don't know if I am correct. I am teaching my cousin, but I have left school for 20 years

 

[kenny1999]

Another question , I avoid starting a new topic. Am I correct??

 

[PeroK]

OK . This is what I have done, I don't know if I am correct. I am teaching my cousin, but I have left school for 20 years

I think all you need to do is show one interval $(a - \delta, a + \delta)$. You don't need all those different cases. The point $x = 0$ is not important here.

 

[PeroK]

Another question , I avoid starting a new topic. Am I correct??

I guess that's $0 < |x - a| < \delta$?

 

[FactChecker]

To make your diagram more clear, show $a$ on it. Then show $a-\delta$ and $a+\delta$. There is no reason to even show where anything else, like $x=0$, is. Then one diagram takes care of all the cases.

 

[kenny1999]

I think all you need to do is show one interval $(a - \delta, a + \delta)$. You don't need all those different cases. The point $x = 0$ is not important here.

Hi, did you mean I do not have to consider the possible ranges of value of a ? (Since a isn't conditioned but the delta is given that >0, that's why I am wondering if I need to separate a into different ranges of value

 

[kenny1999]

I guess that's $0 < |x - a| < \delta$?

No, "Another question" is really another, not related to the first question, yes the first question was $0 < |x - a| < \delta$

I think the second question does NOT include x=0. How to draw a symbol to represent that x=0 isn't included?? an arrow??

 

[PeroK]

Hi, did you mean I do not have to consider the possible ranges of value of a ? (Since a isn't conditioned but the delta is given that >0, that's why I am wondering if I need to separate a into different ranges of value

You don't have to consider different values for $a$.

 

[PeroK]

No, "Another question" is really another, not related to the first question, yes the first question was $0 < |x - a| < \delta$

I think the second question does NOT include x=0. How to draw a symbol to represent that x=0 isn't included?? an arrow??

It's $x =a$ that is excluded. I would just use $(a-\delta, a)(a, a + \delta)$ with round brackets to show the end points are excluded.