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Mathematics

The solution set for 0 < −x3-\dfrac{x}{3} < 2, x ∈ Z is;

  1. {-5, -4, -3, -2, -1}

  2. {-6, -5, -4, -3, -2, -1}

  3. {-5, -4, -3, -2, -1, 0}

  4. {-6, -5, -4, -3, -2, -1, 0}

Linear Inequations

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Answer

Given, 0 < −x3-\dfrac{x}{3} < 2

Solving L.H.S. of equation :

⇒ 0 < −x3-\dfrac{x}{3}

⇒ x3\dfrac{x}{3} < 0

⇒ x < 0 × 3

⇒ x < 0………………. (1)

Solving R.H.S. of equation :

⇒ −x3-\dfrac{x}{3} < 2

⇒ -x < 2 × 3

⇒ -x < 6

⇒ x > -6 ……………….. (2)

From, equation (1) and (2), we get

-6 < x < 0 and x ∈ Z.

Solution set for x = {-5, -4, -3, -2, -1}.

Hence, option 1 is the correct option.

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