Question

If the replacement set is the set of natural numbers, solve.

(i) x – 5 < 0

(ii) x + 1 < 7

(iii) 3x – 4 > 6

(iv) 4x + 1 > 17

Answer 1

(i) x – 5 < 0 x – 5 + 5 <0 + 5 ………(Adding 5)

=> x < 5

Required answer = {1, 2, 3, 4}

(ii) x + 1 ≤ 7 => x + 1 – 1 ≤ 7 – 1 ( Subtracting 1)

=> x ≤ 6

Required answer = {1, 2, 3, 4, 5, 6}

(iii) 3x – 4 > 6 3x – 4 + 4 > 6 + 4 (Adding 4)

=> 3x > 10 > …(Dividing by 3)

3x/3 > 10/3

=> x > 10/3

=> x > 3 1/3

Required answer = { 4, 5, 6, …}

(iv) 4x + 1 ≥ 17

=> 4x + 1 – 1 ≥ 17 – 1 ( Subtracting)

=> 4x ≥ 16

=> 4x/4 ≥ 16/4 (Dividing by 4)

=> x ≥ 4

Required answer = {4, 5, 6, …}