- In mathematics, an inequality is a relation that holds between two values when they are different
- Solving linear inequalities is very similar to solving linear equations, except for one small but important detail: you flip the inequality sign whenever you multiply or divide the inequality by a negative

- The symbol < means less than. The symbol > means greater than.
- The symbol < with a bar underneath means less than or equal to. Usually this is written as $\leq$
- The symbol > with a bar underneath means greater than or equal to. Usually this is written as $\geq$
- The symbol $\neq$ means the quatities on left and right side are not equal

- a < b means a is less then b or b is greater a
- $a \leq b$ means a is less then or equal to b
- a > b means a is greater than b
- $a \geq b$ means a is greater or equal to b

- addition of same number on both sides

$a > b $

=> $a+c > b +c $

- Substraction of same number on both sides

$a > b$

=>$a-c > b-c$ - Multipication/Division by same positive number on both sides

$a > b$

if c is positive number then

$ac > bc$

or

$\frac {a}{c} > \frac {b}{c}$

- swapping the left and right sides
- Multiplication/Division by negative number on both sides
- Dont multiple by variable whose values you dont know as you dont know the nature of the variable

- A number line is a horizontal line that has points which correspond to numbers. The points are spaced according to the value of the number they correspond to; in a number line containing only whole numbers or integers, the points are equally spaced.

- It is very useful in solving problem related to inequalities and also representing it

Suppose x >2(1/ 3), this can represent this on number line like that

$ ax+b > 0 $

or

$ax+b \geq 0$

or

$ax+b< 0$

or

$ax+b \leq 0$

are called the linear equation in One Variable

- $x-2 < 0 $
- $3x +10 > 0$
- $10x-17 \geq 0$

$ax+by > c$

or

$ax+by \geq c$

or

$ax+by< c $

or

$ax+by \leq c$

are called the linear equation in two Variable

- $x-2y < 0 $
- $3x +10y > 0 $
- $10x-17y \geq 0$

**Notes**- What are inequalities
- Things which changes the direction of the inequality
- Linear Inequation in One Variable
- Linear Inequation in Two Variable
- Steps to solve the inequalities in one variable
- Steps to solve the inequality of the another form
- Quadratic Inequation
- Steps to solve Quadratic or polynomial inequalities
- Cubic Inequation
- Steps to solve Cubic inequalities
- Absolute value equation
- Absolute value inequation
- Graphical Solution of Linear inequalities in Two Variable

**NCERT Solutions**