The addition theorem of probability consists of two formulas. One is when both the events are mutually exclusive and the other represents when both the events are not exclusive. Addition theorems for n events are described below.

Linear inequalities, in mathematics, involve linear functions. In these functions, both sides are not equal and therefore, can not be represented with an equal sign. Generally, inequality can be an algebraic inequality or a generic inequality or can be both.

Linear inequality definition consists of those expressions one which both sides are not equal. Here, the equal sign is replaced by a greater than symbol, less than symbol, greater than or equal to symbol and less than or equal to symbol. There are different types of inequality as well. They are polynomial inequality, absolute value inequality, rational inequality.

## How to solve inequalities?

Step 1: The inequality must be written in the form of an equation.

Step 2: The formed equation is solved for one or more values

Step 3: All the values are then expressed in the number line.

Step 4: Generally, open circles are used in the number lines to show excluded values of the equation.

Step 5: The interval is found.

Step 6: Now, any random value from the range is taken and placed in the inequation to exhibit whether the value satisfies the inequation.

Step 7: Therefore, the interval will satisfy the in

equation and that is the answer.

## System of linear inequalities

A system of linear inequalities consists of at least two linear inequations with identical variables. Those can be solved to obtain certain answers and functions as well.

## Linear inequality calculator:

Linear inequality calculator comprises any online tool which solves the equations so that the user doesn’t have to solve that manually.

## How to use a linear inequality calculator?

The step by step procedure to use the linear inequalities calculator for users is as follows:

Step 1: Firstly, one has to put the inequations in the input gap

Step 2: Now, the solve button should be clicked to obtain the required number line.

Step 3: After that, the number line will be shown on the screen.

## Example

Solve the inequality 4 ( x + 2 ) − 1 > 5 − 7 ( 4 − x )

Solution: Given,

4 ( x + 2 ) − 1 > 5 − 7 ( 4 − x )

Expanding the brackets and multiplying by each term we get;

4 x + 8 − 1 > 5 − 28 + 7 x

or, 4 x + 7 > − 23 + 7 x

Subtract 7 on both the sides

4x + 7 – 7 > -23 + 7x – 7

or, 4x > -30 + 7x

Subtracting 7x from both the sides

or, 4x – 7x > -30 + 7x – 7x

or, − 3 x > − 30

Multiplying both the sides by -1, the inequality gets reversed;

-3x (-1) < -30 x (-1)

Or, 3x < 30

Dividing both the sides by 3, we get;

3x/3 < 30/3

Or, x < 10

Hence, x lies between -∞ and less than 10.

### Conclusion:

Linear inequalities are those linear functions whose both sides are not equal to each other. Though the inequalities are different from equations, the calculation of inequalities is quite simple and is similar to that of equations. A system of linear inequalities consists of at least two linear inequations with identical variables.

Get answers to the most common queries related to the CBSE 11th Examination Preparation.

## Write the mathematical expression of the addition theorem for two exclusive events?

Ans. P (A∪B) = P(A)+ P(B)