Question

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 ≥ 5
⇒ x ≤ 5
∴ Solution set = {1, 2, 3, 4, 5}

Options

• A is true, R is false.

• A is false, R is true.

• Both A and R are true and R is the correct reason for A.

• Both A and R are true and R is the incorrect reason for A.

Answer 1

A is false, R is true.

Explanation:

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

⇒ 5 − 2x + 10 ≥ x

⇒ −2x + 15 ≥ x

⇒ 15 ≥ x + 2x

⇒ 15 ≥ 3x

⇒ x ≤ 153315​

⇒ 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.