Dear Henryt999,
We have to find such that,
As you have mentioned, -------------A
Similarly,
Therefore, --------------B
From A and B, and
Therefore, and
So we would get, as the answer.
Hope this helps.
Hi thanks in advance.
I canīt grasp what the inequality is asking for?
For what positive number (s) is the following statement true?
(those strange I:s represent abs: )
I solved
That gives me / add +4
And now I donīt understand what I am suppose to do.
Dear Henryt999,
We have to find such that,
As you have mentioned, -------------A
Similarly,
Therefore, --------------B
From A and B, and
Therefore, and
So we would get, as the answer.
Hope this helps.
Hello, Henryt999!
Note that: .For what positive number is the following statements true?
. .
From [1], we have: . .[3]
From [2], we have: . .[4]
[3] tells us that is between andCode:- - - o = = = = = = o - - - 3-s 3+s
[4] tells us that is between 2 and 6.Code:- - o = = = = = = = = o - - 2 6
For both statements to be true,
. . the first interval must be "inside" the second interval.Code:- - - o = = = = = = o - - - 3-s 3+s - - o = = = = = = = = o - - 2 6
So we have: .
. . which are both true for: .
Therefore, the inequalities are true for: .
Dear Sorban,
You had considered the situation where the 3-s<x<3+x is inside 2<x<6. But I have considered the situation where 2<x<6 is inside 3-s<x<3+x. I think both situations must be considered since in both situations, the two inequalities hold.
Therefore the answer could be either, or
[QUOTE=Henryt999;445369]For what positive number (s) is the following statement true? [/QUOTE
Sudharaka, the solution Sorban gave is correct and is the only solution.
I think that you have misread the question or you failed to see the implication.
is the set of numbers .
is the set of numbers .
The implication in the question, , means that .
We know that but we cannot have .
For then we would have but .
You want to find all values of for which is true.