Question 3:
Solve 5x– 3 < 7, when
(i) x is an integer (ii) x is a real number
Answer
The given inequality is 5x– 3 < 7.
−12x > 30
⇒ 5x – 3 + 3 < 7 + 3
⇒ 5x < 10
(i) The integers less than 2 are …, –4, –3, –2, –1, 0, 1.
Thus, when x is an integer, the solutions of the given inequality are …, –4, –3, –2, –1, 0, 1.
Hence, in this case, the solution set is {…, –4, –3, –2, –1, 0, 1}.
(ii) When x is a real number, the solutions of the given inequality are given by x < 2,
that is, all real numbers x which are less than 2.
Thus, the solution set of the given inequality is x ∈ (–∞, 2).
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