## Inequalities Mathematical Formulas

One of the most important topic in Competitive math is Inequalities Mathematical Formulas. Few questions will definitely come from this topic.

The sign shows that it is a greater than suppose 5 > 3 which means 5 is bigger than 3.

**Ex.** 5>4, 9> 7

**<**

The sign shows that it is a lesser than suppose 3 < 5 which means 3 is lesser than 5.

**Ex. **4<9, 7<9

**>**

The sign ≥ shows that both are equal also a is greater than b suppose a≥b .

Ex. a > b

**<**

The sign ≤ shows that both are equal also a is lesser than b suppose a≤b ..

Ex.a<b

**Types of Inequalities :**

- a ≤ b => -a≥b
- a ≤ b => a ± c ≤ b ± c

- a ≤ b, c > 0 => ac ≤ bc, a / c ≤ b / c;

a ≤ b , c < 0 => ac ≥ bc, a / c ≥ b / c

- 0 < a < b ⇒ 1 / a > 1 / b > 0

- a < b < 0 ⇒ 0 > 1 / a > 1 / b
- a < 0 < b ⇒ 1 / a < 0 < 1 / b

- a ≤ b ⇔ a
^{n}≤ b^{n}, (n,a,b > 0) - a ≤ b ⇔ a
^{-n}≤ b^{-n} - a ≤ b ⇔ In a ≤ In b

- e
^{x}≥ 1 + x - x
^{x}≥ (1/e)^{1/e}, x ≥ 1 - X
^{xx}≥ x x ≥ 1

- a
^{a}+ b^{b}≥ a^{b}+ b^{a}> 1, a , b > 0

We provide few tricks on Inequalities Mathematical Formulas. Please visit this page to get updates on more Math Shortcut Tricks. You can also like our facebook page to get updates.

If you have any question regarding Inequalities Mathematical Formulas then please do comment on below section. You can also send us message on facebook.