Question

Assertion: If the same number or expression is added to both sides of an inequation, the resulting inequation has the same sign of inequality as that of the original.

Reason: −5 (x − 9) ≥, 17 − 9x > x + 2, x ∈ R gives Х ∈ `[-7, -3/2]`

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

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

Explanation:

Given:

−5(x − 9) ≥ 17 − 9x > x + 2, x ∈ R

First part:

−5(x − 9) ≥ 17 − 9x

⇒ −5x + 45 ≥ 17 − 9x

⇒ −5x + 45 − 17 ≥ − 9x

⇒ 28 ≥ −4x

⇒ x ≥ −7

Second part:

17 − 9x > x + 2

⇒ 17 − 2 > x + 9x

⇒ 15 > 10x

⇒ x < `3/2`

Combine both:

`x ∈ (-7, 3/2)`

Reason is false.