**Inequalities Mathematical Formulas**

**>**

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

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