CLASS-8INTRODUCTION OF LINEAR IN EQUATIONS

INEQUATIONS

An inequality is a mathematical statement showing that two expressions are not equal, for example, 5 > 2 and 7 < 9, the symbols of inequality are represented in the following table.

Symbols of inequality

Symbol                              Meaning

>                               is greater than

<                                 is less than

≥                           is greater than or equal to

≤                            is less than or equal to

An inequality involving at least one variable which can take on some values to make the statement true, is called an inequation.

Linear Inequations –

A linear equations in one variable, say ‘x’, is of the form ax + b > c, where the symbol > can be replaced by any of the other symbols of inequality shown above.

There are some examples given for better understanding –

Example.1)    7x + 4 < 8

Example.2)   15x + 7 < 3 – 5x

Example.3)   10 – 5x > 8

Example.4)   8x – 19 > 25x – 4

Replacement Set –

The set from which the values of the variable are to be selected to make an in-equation true, is called the replacement set or domain of the variable.

Example.1) If x< 2 and x Є W ( the set of whole numbers) then the values of ‘x’ are to be selected from the set W, which is the replacement set for the inequation.

2) If x ≥ 4 and x Є { 2, 3, 4, 5, 6, 7 } then the set { 2, 3, 4, 5, 6, 7 } is the replacement set from which the values of x are to be selected.

Solution Set –

The solution set or truth set of an inequation is a set of numbers each element of which, when substituted for the variable, makes the inequality true.

Examples.1) Consider the inequation x ≥ 2, x Є N.

The replacement set = N = { 1, 2, 3, ……….. }

Out of the set N, the values 2, 3, 4, ……..satisfy the inequation, that is, make the inequality true.

So, the solution set is = { 2, 3, 4, ……….. }

Examples.2) Consider the inequation x ≤ 2, x Є { -3, -2, 2, 4, 5 }

The replacement set = { -3, -2, 2, 4, 5 }

Only the values -3, -2, and 2 from the replacement set satisfy the inequation.

So, the solution set =  { -3, -2, 2 }