If a>0 and b<0, then |a-b|=a-b

Question

I need help with this proof. I don't know what to do

Answer 1

a>0 means a always positive number, for example +5

b<0 means b always negative number ( it has negative sign), for example -8

b-a = 5 - (-8) = 13 that's mean your answer will be always positive

so when you take the absolute value for positive number it will make no difference,

Therefore | a - b | = a - b.

Answer 2

You are being asked to show | a - b | = a - b.

So, think about that expression, a - b, as just a number (since that's what it is, right?).

What kind of number has an absolute value that just = itself?

Can you show that the number a - b is that kind of number?