I'm given the following: If $|x-y|≤2$ then $|y-x|≤2$. How would I go about proving $|y-x|≤2$?
The answer I came up with: If $|x-y|≤2$ then $|y-x|≤2$. By saying $|x-y|≤2$, we are saying that x and y are within 2 integer value places of one another, and because of the absolute value operation and commutative property of addition, it doesn’t matter in which order you place x and y, if they are within 2 integer values of one another, it will be less than or equal to 2. As shown above, x and y are associated within Thus, if $|x-y|≤2$ then $|y-x|≤2$.
Even though I can tell $|x-y|≤2$ then $|y-x|≤2$ is true, I'm not sure if my above answer fully justifies concluding that $|y-x|≤2$. I've been working on the problem and came up with inequality relationships for x and y, but wasn't sure if or how I could apply them.
