debbie394
Badges: 10
Rep:
?
#1
Report Thread starter 3 years ago
#1
Question: http://pmt.physicsandmathstutor.com/...dulus%20QP.pdf
Question 2

Answer: http://pmt.physicsandmathstutor.com/...dulus%20MS.pdf

My Question:
what does question 2 mean and how do you answer it?
0
reply
_JB_
Badges: 9
Rep:
?
#2
Report 3 years ago
#2
Clue: What is the equivalent form of |x-a| < b. Probably want to go through your book

Edit: Your answer already tells you everything you need to know.
0
reply
debbie394
Badges: 10
Rep:
?
#3
Report Thread starter 3 years ago
#3
(Original post by _JB_)
Clue: What is the equivalent form of |x-a| < b. Probably want to go through your book

Edit: Your answer already tells you everything you need to know.
Where did the -1<x-2<1 come from??



1 < x  2 < 1



1 < x  2 < 1
0
reply
_JB_
Badges: 9
Rep:
?
#4
Report 3 years ago
#4
One of the inequality rules stat that: if a < b, then a - c < b - c.

Do you think you can do this? If a < b < c, then a - d < b - d < c - d.
0
reply
debbie394
Badges: 10
Rep:
?
#5
Report Thread starter 3 years ago
#5
(Original post by _JB_)
One of the inequality rules stat that: if a < b, then a - c < b - c.

Do you think you can do this? If a < b < c, then a - d < b - d < c - d.
why choose 2?
0
reply
mupsman2312
Badges: 11
Rep:
?
#6
Report 3 years ago
#6
(Original post by esmeralda123)
Question: http://pmt.physicsandmathstutor.com/...dulus%20QP.pdf
Question 2

Answer: http://pmt.physicsandmathstutor.com/...dulus%20MS.pdf

My Question:
what does question 2 mean and how do you answer it?
The question just wants you to write the inequality in a different form.

The value of a will just be the mid-point of the original range, as you'll want to have the same value of |x-a| for both x=1 and x=3 (namely b). Then simply substitute this value of a and x=1 or x=3 to obtain the value of b (remember that, as |x-a| > 0, b>0 also).

Alternatively, can get to the values of a and b as follows (this is probably a better way of thinking about it and setting it out):

Spoiler:
Show


|x-a| < b is the same as saying that -b < x-a < b. You want to put the original equation into this form. You currently have 1<x<3. The width of this range is 3-1 = 2, and the width of our algebraic range is b-(-b) = b+b = 2b. The two ranges should be equivalent, so we have 2b = 2, i.e. b = 1. Thus, we now have -1 < x-a < 1. Adding a to each part of this inequality, we get a-1 < x < a+1. But, 1<x<3. Hence, a-1 = 1 and a+1 = 3; both equations yield the solution a = 2.

You can now simply double-check in your head that this solution works by substituting suitable values of x.

As you get more used to these types of questions, you should be able to see the value of a straightaway - i.e. the value of a for which substituting the limits of the original inequality will give you |(plus/minus the same value)| = (the same value). In the mark scheme, they've seen immediately that subtracting 2 from the original inequality gives you +1 as the strict limits of the inequality. Hence a=2 and b=1 (as +b = +1).

I hope that this explanation is clear enough for you - it can be slightly tricky to explain...
0
reply
_JB_
Badges: 9
Rep:
?
#7
Report 3 years ago
#7
So the left side is -1 and right side is +1?

|x - 2| < 1 is equivalent to -1 < x - 2 < 1.

I will use a simpler example:
|x| < 2 means the absolute value of x is less than 2. Mean x can be 1.8, -1.5 etc etc.
Then you can deduce that |x| < 2 and -2 < x < 2 is equivalent.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

Do you think receiving Teacher Assessed Grades will impact your future?

I'm worried it will negatively impact me getting into university/college (70)
38.04%
I'm worried that I’m not academically prepared for the next stage in my educational journey (18)
9.78%
I'm worried it will impact my future career (12)
6.52%
I'm worried that my grades will be seen as ‘lesser’ because I didn’t take exams (45)
24.46%
I don’t think that receiving these grades will impact my future (24)
13.04%
I think that receiving these grades will affect me in another way (let us know in the discussion!) (15)
8.15%

Watched Threads

View All
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise