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Mathematics

Inequation 5 - 2x ≥ x - 10, where x ∈ N (Natural numbers)

Assertion (A): 5 - 2x ≥ x - 10 ⇒ -3x ≥ -15 ⇒ x ≥ 5

∴ Solution set = {5, 6, 7, 8, ……….}

Reason (R): 5 - 2x ≥ x - 10 ⇒ 5 + 10 ≥ 3x ⇒ x ≤ 5

∴ Solution set = {1, 2, 3, 4, 5}

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true and R is correct reason for A.

  4. Both A and R are true and R is incorrect reason for A.

Linear Inequations

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Answer

A is false, R is true.

Reason

According to Assertion: 5 - 2x ≥ x - 10

⇒ 5 - 2x + 10 ≥ x

⇒ -2x + 15 ≥ x

⇒ 15 ≥ x + 2x

⇒ 15 ≥ 3x

⇒ x ≤ 153\dfrac{15}{3}

⇒ x ≤ 5

∴ Solution set = {1, 2, 3, 4, 5}

So, Assertion (A) is false.

According to Reason:

Solution set = {1, 2, 3, 4, 5}

So, Reason (R) is true.

Hence, A is false, R is true.

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