If x ∈ N, find the solution set of each of the following inequations : (i) 4x 13 (ii) 2x - 9 -1 (iii) 3 - x -2 (iv) 5 - 7x - 16 (v) - 2 (vi)

Question

KnowledgeBoat · Accepted Answer

(i) 4x 13 We have: ⇒ 4x 13 ⇒ x ⇒ x 3.25 Natural numbers less than 3.25 are {1, 2, 3}. ∴ Solution set = {1, 2, 3} (ii) 2x - 9 -1 We have: 2x - 9 -1 ⇒ 2x -1 + 9 [Adding 9 on both sides] ⇒ 2x 8 ⇒ x ⇒ x 4 Natural numbers less than 4 are {1, 2, 3}. ∴ Solution set = {1, 2, 3} (iii) 3 - x -2 We have: 3 - x -2 ⇒ -x -2 - 3 [Subtracting 3 from both sides] ⇒ -x -5 ⇒ x 5 [Multiplying -1 on both sides and reversing the sign] Natural numbers greater than 5 are {6, 7, 8, 9, ...} ∴ Solution set = {6, 7, 8, 9, ...} (iv) 5 - 7x - 16 We have: 5 - 7x - 16 ⇒ -7x -16 - 5 [Subtracting 5 from both sides] ⇒ -7x -21 Dividing by a negative number reverses the inequality: ⇒ x ⇒ x 3 Natural numbers less than 3 are {1, 2} ∴ Solution set = {1, 2} (v) - 2 We have: Natural numbers less than 10.28 are {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. ∴ Solution set = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (vi) We have: Natural numbers greater than 2.25 are {3, 4, 5, ...} ∴ Solution set = {3, 4, 5, ...}

Mathematics

If x ∈ N, find the solution set of each of the following inequations : (i) 4x 13 (ii) 2x - 9 -1 (iii) 3 - x -2 (iv) 5 - 7x - 16 (v) - 2 (vi)

Linear Inequations

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