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Mathematics

The solution for 1 < 3 - 2x ≤ 7; x ∈ N (Natural numbers) is :

  1. {8}

  2. {-1, -2}

  3. { }

  4. {1}

Linear Inequations

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Answer

Given,

Inequation : 1 < 3 - 2x ≤ 7

Solving L.H.S. of the inequation :

⇒ 1 < 3 - 2x

⇒ 2x < 3 - 1

⇒ 2x < 2

⇒ x < 22\dfrac{2}{2}

⇒ x < 1 …………….(1)

Solving R.H.S. of the inequation :

⇒ 3 - 2x ≤ 7

⇒ 2x ≥ 3 - 7

⇒ 2x ≥ -4

⇒ x ≥ −42-\dfrac{4}{2}

⇒ x ≥ -2 ……………..(2)

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

-2 ≤ x < 1 and x ∈ N.

So, Solution set is an empty set.

Hence, Option 3 is the correct option.

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