If x ∈ {-2, -1, 0, 1, 2, 3, 4, 5}, find the solution set of each of the following inequations : (i) 2x 5 (ii) 3x - 8 1 (iii) 3 - 12x -21 (iv) 7 - x 0 (v) 3 - 4x -2 (vi) 3x + 4 15 (vii) - 1 (viii) - (ix)

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(i) 2x 5 We have : 2x 5 ⇒ x ⇒ x 2.5 From the set, values greater than 2.5 are {3, 4, 5}. ∴ Solution set = {3, 4, 5} (ii) 3x - 8 1 We have: 3x - 8 1 ⇒ 3x 1 + 8 [Adding 8 on both sides] ⇒ 3x 9 ⇒ x ⇒ x 3 From the set, values less than 3 are {-2, -1, 0, 1, 2}. ∴ Solution set = {-2, -1, 0, 1, 2} (iii) 3 - 12x -21 We have: 3 - 12x -21 ⇒ -12x -21 - 3 [Subtracting 3 from both sides] ⇒ -12x -24 Dividing by a negative number reverses the sign: ⇒ x ⇒ x 2 From the set, values less than 2 are {-2, -1, 0, 1}. ∴ Solution set = {-2, -1, 0, 1} (iv) 7 - x 0 We have: 7 - x 0 ⇒ 7 x ⇒ x 7 All values in the set are less than 7. ∴ Solution set = {-2, -1, 0, 1, 2, 3, 4, 5} (v) 3 - 4x -2 We have: 3 - 4x -2 ⇒ -4x -2 - 3 [Subtracting 3 from both sides] ⇒ -4x -5 Dividing by a negative number reverses the sign: ⇒ x ⇒ x 1.25 From the set, values less than 1.25 are {-2, -1, 0, 1}. ∴ Solution set = {-2, -1, 0, 1} (vi) 3x + 4 15 We have: 3x + 4 15 ⇒ 3x 15 - 4 [Subtracting 4 from both sides] ⇒ 3x 11 ⇒ x ⇒ x 3.66... From the set, values less than 3.66... are {-2, -1, 0, 1, 2, 3}. ∴ Solution set = {-2, -1, 0, 1, 2, 3} (vii) - 1 We have: - 1 ⇒ 3x -1 x 4 [Multiplying 4 on both sides] ⇒ 3x -4 ⇒ x ⇒ x -1.33... From the set, values greater than -1.33... are {-1, 0, 1, 2, 3, 4, 5}. ∴ Solution set = {-1, 0, 1, 2, 3, 4, 5} (viii) - We have: From the set, values less than -0.833 are {-2 , -1}. ∴ Solution set = {-2, -1} (ix) We have: From the set, values greater than 0.305... are {1, 2, 3, 4, 5}. ∴ Solution set = {1, 2, 3, 4, 5}

Mathematics

If x ∈ {-2, -1, 0, 1, 2, 3, 4, 5}, find the solution set of each of the following inequations : (i) 2x 5 (ii) 3x - 8 1 (iii) 3 - 12x -21 (iv) 7 - x 0 (v) 3 - 4x -2 (vi) 3x + 4 15 (vii) - 1 (viii) - (ix)

Linear Inequations

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