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Mathematics

Find the smallest value of x for the inequation x - 3(2 + x) < 2(3x - 1) when :

(i) x ∈ W (whole numbers)

(ii) x ∈ N (natural numbers)

(iii) x ∈ I (integers)

Linear Inequations

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Answer

⇒ x - 3(2 + x) < 2(3x - 1)

⇒ x - 6 - 3x < 6x - 2

⇒ -2x - 6 < 6x - 2

⇒ 6x + 2x > -6 + 2

⇒ 8x > -4

⇒ x > −48-\dfrac{4}{8}

⇒ x > −12-\dfrac{1}{2}

(i) Since, x ∈ W and x > −12-\dfrac{1}{2}

∴ x = 0.

Hence, x = 0.

(ii) Since, x ∈ N and x > −12-\dfrac{1}{2}

∴ x = 1.

Hence, x = 1.

(iii) Since, x ∈ I and x > −12-\dfrac{1}{2}

∴ x = 0.

Hence, x = 0.

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