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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