Modulus

Question: http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/OCR-MEI/C3%20Functions%20-%20Modulus%20QP.pdf
Question 2

Answer: http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/OCR-MEI/C3%20Functions%20-%20Modulus%20MS.pdf

My Question:
what does question 2 mean and how do you answer it?

Reply 1

_JB_

9

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.

(edited 6 years ago)

Reply 2

debbie394

OP

11

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

Reply 3

_JB_

9

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.

Reply 4

debbie394

OP

11

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?

Reply 5

mupsman2312

11

Original post by esmeralda123

Question: http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/OCR-MEI/C3%20Functions%20-%20Modulus%20QP.pdf
Question 2

Answer: http://pmt.physicsandmathstutor.com/download/Maths/A-level/C3/Topic-Qs/OCR-MEI/C3%20Functions%20-%20Modulus%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

(edited 6 years ago)

Reply 6

_JB_

9

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.

Modulus

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