Question

Assertion: The solution set of 7 + 3x ≤ 35 − 2x, x ∈ W is {0, 1, 2, 3, 4, 5}

Reason: W = {0, 1, 2, 3, 4, ...}

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation:

7 + 3x ≤ 35 − 2x

3x + 2x ≤ 35 − 7

⇒ 5x ≤ 28

⇒ x ≤ `28/5`

= 5.6

Given x ∈ W

Whole numbers:

W = {0, 1, 2, 3, 4, 5, …}

Whole numbers less than or equal to 5.6 are:

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

Assertion (A) is true.

W = {0, 1, 2, 3, 4, …}

Reason (R) is true, and it helps explain why only those values are included.