On Page 96 of the Math Essentials Blue Book 0.

I do not understand the last comment, "Again, you can reform the bracketing inequalities found above if you wish:"

What does "reform" mean?

For example, how does y< x+2 become, x+2<y?

I believe what they mean is that you can go from a trio of inequalities, like y-2 < x < 2y+1
to two pairs of inequalities, like
y-2 < x and x < 2y+1
and simplify both of these until they become
y < x+1 and y > (x-1)/2
And then you can re-combine the three of them:
(x-1)/2 < y < x+1

You can't, however, go from y< x+2 to x+2<y. These two statements are directly opposite each other.

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