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INTRODUCTION OF LINEAR INEQUATIONS

**LINEAR INEQUATIONS –**

**A statement of inequality between two expressions involving
a single variable x with highest power 1, is called a linear inequations.**

**The general forms of linear inequations are –**

**(i) ax + b < c, (ii) ax + b ≤ c, (iii) ax + b > c, (iv) ax + b ≥ c**

**Where a, b, c are real numbers and a ≠ 0.**

__Replacement Set or Domain of the Variable –__

**The set from which the values of the variable x are replaced
in an inequation, is called or to be considered as the replacement set or the
domain of the variable. This kind of replacement set is always given to us.**

__Solution Set –__

**The set of all those values of x from the replacement set
which satisfy the given inequation, is called the solution set of the
inequation.**

**It has been considered that, solution set is always a subset
of the replacement set.**

**Example- write down the solution set of x < 5, when the
replacement set is (i) N, (ii) W, (iii) I**

**Solution - (i)
Solution set = {x ϵ N : x < 5} = {1, 2, 3, 4}**

** (ii) Solution set = {x ϵ W : x <
5} = {0, 1, 2, 3, 4}**

** (iii) solution set = {x ϵ I : x < 5} = {……., -2, -1, 0, 1, 2, 3, 4}**

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