Proof Help: Converting Inequality from sn ≤ M < A to |sn - A| ≥ A - M

[Jamin2112]

Homework Statement

I reached the point of

s_n ≤ M < A

and I need to get to

|s_n - A| ≥ A - M

before I can move on and reach my final conclusion.

(Don't worry about what I'm trying to prove; just help me on this little step)

Homework Equations

Not sure because I've never worked with a 3-thing'd inequality a ≤ b < c.

The Attempt at a Solution

I mean, it's obvious looking at the problem on a number line. The steps just aren't coming to me ...

 

[hunt_mat]

You know that:
$$s_{n}-A\leqslant M-A$$
Also
$$A-s_{n}\geqslant A-M$$
What can we say from this?

 

[Jamin2112]

You know that:
$$s_{n}-A\leqslant M-A$$
Also
$$A-s_{n}\geqslant A-M$$
What can we say from this?

We can't say |A - s_n| ≥ A - M