If x ∈ Z+, find the solution set of each of the following inequations. Represent each solution set on the number line. (i) 7x 17 (ii) 4x - 11 5 (iii) 8 - x (iv) 4(x + 5) 29 (v) 5 x (vi) 2 -

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KnowledgeBoat · Accepted Answer

(i) 7x 17 We have: 7x 17 ⇒ x ⇒ x 2.42... Positive integers less than 2.42... are {1, 2} ∴ Solution set = {1, 2} (ii) 4x - 11 5 We have: 4x - 11 5 ⇒ 4x 5 + 11 [Adding 11 on both sides] ⇒ 4x 16 ⇒ x ⇒ x 4 Positive integers less than 4 are {1, 2, 3} ∴ Solution set = {1, 2, 3} (iii) 8 - x We have: Positive integers less than 7.66.. are {1, 2, 3, 4, 5, 6, 7} ∴ Solution set = {1, 2, 3, 4, 5, 6, 7} (iv) 4(x + 5) 29 We have: 4(x + 5) 29 ⇒ 4x + 20 29 ⇒ 4x 29 - 20 [Subtracting 20 from both sides] ⇒ 4x 9 ⇒ x ⇒ x 2.25 Positive integers less than 2.25 are {1, 2} ∴ Solution set = {1, 2} (v) 5 x We have: 5 x ⇒ 5 x 3 2x [Multiplying 3 on both sides] ⇒ 15 2x ⇒ x [Dividing both sides by 2] ⇒ 7.5 x ⇒ x 7.5 Positive integers less than 7.5 are {1, 2, 3, 4, 5, 6, 7} ∴ Solution set = {1, 2, 3, 4, 5, 6, 7} (vi) 2 - We have: Positive integers greater than 1.38 are {2, 3, 4, 5, ...} ∴ Solution set = {2, 3, 4, 5, ...}

Mathematics

If x ∈ Z+, find the solution set of each of the following inequations. Represent each solution set on the number line. (i) 7x 17 (ii) 4x - 11 5 (iii) 8 - x (iv) 4(x + 5) 29 (v) 5 x (vi) 2 -

Linear Inequations

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