How to solve inequality

The following points have to be kept in mind while solving inequalities:

The modulus of x, |x| equals the maximum of x and –x
For any two real numbers 'a' and 'b', |a|+|b| $$\geq$$ |a+b|
For any real number 'a', $$a^2$$ = $$|a|^2$$

For any positive real number, x+$$\frac{1}{x} \geq$$ 2

For any real number x > 1, 2 < $$(1+\frac{1}{x})^{x}$$ < 2.8. As x increases, the function tends to an irrational number called 'e' which is approximately equal to 2.718.

For any three real numbers X, Y and Z; if X > Y then X+Z > Y+Z

If X > Y and

Z is positive, then XZ > YZ
Z is negative, then XZ < YZ
If X and Y are of the same sign, $$\frac{1}{X}$$ < $$\frac{1}{Y}$$
If X and Y are of different signs, $$\frac{1}{X}$$ > $$\frac{1}{Y}$$