Pre Calculus chapter 1

N

nencyrpatel

New member
Joined
Feb 10, 2020
Messages
4
I need help with this question:
write an absolute value inequality to describe: 6 is at most 3 units from x
 
Hello, and welcome to FMH! :)

Can you show or describe the interval on which \(x\) must lie?
 
This says that you are on the number 6. To find an allowable x value you can only go (from 6) at most three to the right or at most three to the left. So which values can x be???? Please think about this. It is very doable but requires some thought.
 
nencyrpatel said:
I need help with this question:
… 6 is at most 3 units from x
Click to expand...
Hi nencyrpatel. The phrase "is at most 3" means "less than or equal to 3".

Also, an absolute-value inequality in the form

| expression | ≤ C

where C is a positive constant means that the value of expression lies somewhere between -C and C, inclusive. In other words, it means

-C ≤ expression ≤ C

without the absolute-value symbols.

Do you know how to express the distance from some number x to the number 6?

\(\;\)
 
nencyrpatel said:
I need help with this question:
write an absolute value inequality to describe: 6 is at most 3 units from x
Click to expand...
If I wrote:

\(\displaystyle | a - x | \ \le \ b \)

How would you interpret it in words (using the similar construct of your question).
 
I think that it is important for the OP to know the following (basically the answer to Subhotosh's question).

|x-a| < b means that the distance from a to x (or x to a) is less than or equal to b. How would you draw this on a number line?
 
Moreover, the absolute value is a metric. The metric is distance.
\(|x-y|\) is the symbolic notation for the distance between \(x~\&~y\).
Because betweeness is commutative we get at once \(|x-y|=|y-x|\).
The statement that \(|x-6|<1\) means the distance between \(x~\&~6\) is less than 1.
Now the statement that \(|-7|=7\) follows from the notation.
\(7=|0-7|=|-7|\) because 7 is seven units from zero.
 
pka said:
Moreover, the absolute value is a metric. The metric is distance.
\(|x-y|\) is the symbolic notation for the distance between \(x~\&~y\).
Because betweeness is commutative we get at once \(|x-y|=|y-x|\).
The statement that \(|x-6|<1\) means the distance between \(x~\&~6\) is less than 1.
Now the statement that \(|-7|=7\) follows from the notation.
\(7=|0-7|=|-7|\) because 7 is seven units from zero.
Click to expand...
would it be |x-3|<6
 
nencyrpatel said:
would it be [3-x]<6
3-x is greater than or equal to 6
Click to expand...
No! I had asked:

If I wrote:​
​
|a−x| ≤ b|a−x| ≤ b​
​
How would you interpret it in words (using the similar construct of your question).​

You have answered some other question!!
 
Subhotosh Khan said:
No! I had asked:

If I wrote:​
​
|a−x| ≤ b|a−x| ≤ b​
​
How would you interpret it in words (using the similar construct of your question).​

You have answered some other question!!
Click to expand...
the absolute value of the distance between a-x is greater than or equal to b
 
< is less than.
> is greater than.
|x-3|<6 means the distant between x and 3 is 6. Is this what you want?
 
You must log in or register to reply here.
Top