Question

Is |a-b|+|a|-|b| true for all real numbers? explain

Answer 1

Find a counter example?


hmm

|a-b| finds the distance between a and b,

|a|-|b| finds the distance between a and b, such that |a|>|b|
ah ha

so we just need to find a and b such that b>a


b=10
a=5

|a-b|=|5-10|=|-5|=5

|a|-|b|=|5|-|10|=5-10=-5

5≠-5
tada


it is not true for all real numbers
if for all numers such that b>a, it is false