Solve 3x + 8 > 2, when (i) x is an integer (ii) x is a real number.

⇒ 3x + 8 – 8 > 2 – 8 (Rule 1)

⇒ 3x > -6

⇒ > (Rule 2)

⇒ x > -3.

(i) When x is an integer, the following values of x make the statement true.

x = -1, -2, 0, 1, 2, 3, ……

∴ The solution set of the inequality is {-2, -1, 0, 1, 2, 3, ……}

(ii) When x is a real number, the solutions of the inequality are given by x > -3 i. e., all real numbers x which are greater than –3. Therefore, the solution set of the inequality is (-3, ∞ ).

Remarks: Until now we have considered inequalities having solutions as set of natural numbers set of integers as well as the set of real numbers. Henceforth, unless stated other wise, we shall solve the inequalities in the set of real numbers.