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Mathematics

The solution set for -3 < x - 2 ≤ 9, x ∈ Z (integers) is :

  1. {0, 1, 2, 3, 4, ………, 11}

  2. {1, 2, 3, 4, ……., 10}

  3. {-1, 0, 1, 2, 3, ……, 10}

  4. {1, 2, 3, 4, 5, ……., 11}

Linear Inequations

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Answer

Given,

Inequation : -3 < x - 2 ≤ 9

Solving L.H.S. of the above inequation :

⇒ -3 < x - 2

⇒ x > -3 + 2

⇒ x > -1 ………….(1)

Solving R.H.S. of the above inequation :

⇒ x - 2 ≤ 9

⇒ x ≤ 9 + 2

⇒ x ≤ 11 ………..(2)

From (1) and (2),

⇒ -1 < x ≤ 11 and since, x ∈ Z.

Solution set = {0, 1, 2, 3, 4, 5, …….., 11}.

Hence, Option 1 is the correct option.

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