Solve 5x – 3 < 7, when (i) x is an integer. (ii) x is a real number

⇒ 5x – 3 + 3 < 7 + 3 (Rule 1)

⇒ 5x < 10

⇒ < (Rule 2)

⇒ x < 2.

(i) When x is an integer the solutions of the given inequality are .….., -3, -2, -1, 0, 1.

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

(ii) When x is a real number, the solutions of the inequality are given by x < 2 i. e., all real numbers x which are less than 2. Therefore, the solution set of the inequalities is x ∈ (-∞ , 2).