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## 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

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