I have a couple questions, I need to know how to solve these type of problems.

X^2 -4< X + 16

5/n+2 - 5/n = 2/3n

2X^3-x^2-6X + 1/ X^2 + 5x - 8

1) rearragne the terms to get
x^2-x-20<0
(x-5)(x+4)<0
which means that one term can be negative, or -4<x<5 check that.
2) multipy both sides by n(n+2) rearrange terms to see if you can factor and solve as in the first.

3) Is not an equation. It is just an algebraic expression. There is nothng to solve. Did you omit an = sign?