Given that |b − a| = 2 and we need to find which of the following statements must be true?

|b - a| = 2 means that the distance between b and a is 2 units on the number line.

A. a must be positive if b is positive
Let's take example to prove this one right/wrong
If b = 1 then a can be 3 or can be -1
As distance between both (1 and 3) and (1 and -1) on the number line is 2
=> a can be either positive or negative
=> FALSE

B. a must be negative if b is negative
Let's take example to prove this one right/wrong
If b = -1 then a can be 1 or can be -3
As distance between both (-1 and 1) and (-1 and -3) on the number line is 2
=> a can be either positive or negative
=> FALSE

C. b > 0 if a > 2
Let's take example to prove this one right/wrong
If a=2.1 then b can be 0.1 or 4.1
As distance between both (2.1 and 0.1) and (2.1 and 4.1) on the number line is 2
=> In all the cases b will be greater than 0
=> TRUE

So, Answer will be C
Hope it helps!

Watch the following video to learn the Basics of Absolute Values


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