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

**What is inequalities**

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

**Examples**

1)a < b means a is less then b or b is greater a

2) $a \leq b$ means a is less then or equal to b

3) a > b means a is greater than b

4) $a \geq b$ means a is greater or equal to b

**Things are which are safe to do in inequality which does not change in direction**

1) addition of same number on both sides

a > b

=>a+c > b +c

2) Substraction of same number on both sides

a > b

=>a-c > b-c

3) Multipication/Division by same positive number on both sides

a > b

if c is positive number then

ac > bc

or

a/c > b/c

1) swapping the left and right sides

2) Multiplication/Division by negative number on both sides

3) 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

A equation of the form

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

**Example:**

x-2 < 0

or 3x +10 > 0

or $10x-17 \geq 0$

A equation of the form

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

**Example:**

x-2y < 0

or 3x +10y > 0

or $10x-17y \geq 0$

Go Back to Class 11 Maths Home page Go Back to Class 11 Physics Home page

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