Question

For a real numbers a and b, | a - b | = | b - a |.
True or false?

Answer 1

i think it is true

Answer 2

false

Answer 3

example of when it is false, please

Answer 4

@pgpilot326 if you choose random numbers to check , ex. a=8 b=4 8-4=4 but 4-8=-4 , not the same thing ( 4 and -4 )

Answer 5

yes but |8-4| = |4| = |-4| = |4-8|

Answer 6

then pick true , but I think its false

Answer 7

\[|a-b|=|a + (-b)| \le |a| + |-b| = |a| + |b|\]
\[|b-a|=|b + (-a)| \le |b| + |-a| = |b| + |a|\]\[\Rightarrow |a-b|-|b-a| \le 0 \text { by subtracting}\]
\[\text{But } |b-a|-|a-b| \le 0 \text{ must also be true.}\]
\[\text{Therefore }|a-b|-|b-a|=0 \text{ and }|a-b| = |b-a|\]

Answer 8

@Natalieee it's not about what you think, but rather what you can show (or prove). Instincts are a good starting place but they must lead somewhere definitive.