Hi guys, I sometimes troll this forum for information but never post. But I'm really stumped in this 2nd year analysis course. When it comes to proving stuff I just completely suck! I've taken Calc 1-4; Differential Eqns; Linear Algebra; and this is by far the hardest course because I can't seem to wrap my head around the ideas of proving this stuff! Anyway, here are two questions that I hope someone can answer, I'm pretty sure once I see how to do them, I'll be ok.

Question 1:

Let a and b be any real numbers such that a<b and let t be their arithmetic mean. Prove that a<t<b. (t=1/2(a+b))

Question 2:

Solve the inequalities. Justify each step:

x≤5x-4<2x

Now I'm pretty sure these aren't hard questions, but I just don't understand how you can show that.

Any help would be appreciated. Thanks