Question

Find all numbers x for which \[|x-1| + |x-2| > 1\]

Answer 1

I found x > 2 and x < 1

Answer 2

but how do I show this?

Answer 3

|x-1| is the distance from x to 1,
|x-2| is the distance from x to 2.

When is the sum of them equal to 1? when x is between 1 and 2 :-D

Answer 4

1.5 is right if we want those 2 distances equal to 1, but we want greater than 1 :-D

Answer 5

yeah that's why I deleted it, I thought it was >=

Answer 6

I wonder if there is a way to use the fact that\[|x|=\sqrt{x^2}\]

Answer 7

i would do cases

Answer 8

I will post what I have.
Give me a sec.

Answer 9

i hope you can read it

Answer 10

i did 4 cases

Answer 11

and 2 of those cases ended up not to matter

Answer 12

1 case wouldn't work because x can't be greater than 2 and also less than 1 at the same time

Answer 13

another cased got voided because the inequality didn't include equality

Answer 14

case*

Answer 15

right the cases when x is 1 or x is 2 won't work with the inequality

Answer 16

or anything in between those two numbers you mentioned

Answer 17

the solution is (-inf,1) U (2,inf)

Answer 18

did you see my scan?

Answer 19

yeah.

Answer 20

Most interesting was that second case