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Mathematics

If the replacement set = {-6, -3, 0, 3, 6, 9}, find the truth set of the following:
(i) 2x - 1 > 9
(ii) 3x + 7 ≤ 1

Linear Inequations

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Answer

(i) 2x - 1 > 9

⇒ 2x > 9 + 1

⇒ 2x > 10

⇒ x > $\dfrac{10}{2}$

⇒ x > 5

∵ As the replacement set = {-6, -3, 0, 3, 6, 9}.

Hence, solution set = {6, 9}.

(ii) 3x + 7 ≤ 1

⇒ 3x ≤ 1 - 7

⇒ 3x ≤ - 6

⇒ x ≤ - $\dfrac{6}{3}$

⇒ x ≤ - 2

∵ As the replacement set = {-6, -3, 0, 3, 6, 9}.

Hence, solution set = {-6, -3}.

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