Mathematics
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
Linear Inequations
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Answer
(i) x - 5 < 0
⇒ x < 0 + 5
⇒ x < 5
∵ As x is a natural numbers.
Hence, solution set = {1, 2, 3, 4}.
(ii) x + 1 ≤ 7
⇒ x ≤ 7 - 1
⇒ x ≤ 6
∵ As x is a natural numbers.
Hence, solution set = {1, 2, 3, 4, 5, 6}.
(iii) 3x - 4 > 6
⇒ 3x > 6 + 4
⇒ 3x > 10
⇒ x >
⇒ x > 3.33…..
∵ As x is a natural numbers.
Hence, solution set = {4, 5, 6,…….}.
(iv) 4x + 1 ≥ 17
⇒ 4x ≥ 17 - 1
⇒ 4x ≥ 16
⇒ x ≥
⇒ x ≥ 4
∵ As x is a natural numbers.
Hence, solution set = {4, 5, 6,…….}.
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