Question

If x is an integer that satisfies 9 < 4x – 1 ≤ 19, then x is an element of which of the following sets?

(a) {3, 4}

(b) {2, 3, 4}

(c) {3, 4, 5}

(d) {2, 3, 4, 5}

Answer 1

(c) {3, 4, 5}

Given, 9 < 4x – 1 ≤ 19 

⇒ 9 < 4x – 1 and 4x – 1 ≤ 19 

⇒ 9 + 1 < 4x and 4x ≤ 19 + 1 

⇒  x > \(\frac52\) and x ≤ 5 

∴  x < \(\frac52\) ≤ 5

∵ x ∈ Z

 ∴ x = {3, 4, 5}.