If a<b, then Ia-bI (absolute value of a minus b) is equivalent to which of the following?

Question

I know it is -(a-b) but I do not understand why?

Answer 1

Lets first -just in case- clarify what |x| is, Im sorry if I will be telling you too basic things, then just skip this first part and go on below the second serie or stars.

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If x is a positive number or x = 0, then |x| = x
If x is a negative number, then |x| = -x.

Think of this example:

|-4| = 4 = - (-4). - (-4) is a positive number, since its the opposite of -4.

So, -x is a positive number is x is a negative one

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OK. Now to your question

a
So, | a-b | = b-a = - (a-b)

This is why

Ana

Answer 2

Well, first understand what |a-b| means. This means that when you subtract b from a, you make that number positive, whether it is positive or negative.

Now, we know that a
Thus, given this condition, the absolute value must be a positive number, as will be the -(a-b) term, which is why these two are equivalent.

Answer 3

'Absolute value' simply says take a value and, if it's positive do nothing. If it's negative, change the sign to positive. If a < b then a-b will be negative, and the absolute value operator will change the sign so that it will be -(a-b)

Doug