Assertion :|3 x-5| 9 ⇒ x ∈(-∞, (-4/3)) ∪((14/3), ∞) Reason: The region containing all the solutions of an inequality is called the solution region.

Question

Assertion :|3 x-5| > 9 ⇒ x ∈(-∞, (-4/3)) ∪((14/3), ∞) Reason: The region containing all the solutions of an inequality is called the solution region. (A) Assertion is correct, reason is correct; reason is a correct explanation for assertion. (B) Assertion is correct, reason is correct; reason is not a correct explanation for assertion (C) Assertion is correct, reason is incorrect (D) Assertion is incorrect, reason is correct.

Tardigrade Admin · Accepted Answer

We have, |3 x-5| > 9 ⇒ 3 x-5 < -9 or 3 x-5 > 9 ⇒ 3 x < -4 or 3 x > 14 ⇒ x < (-4/3) or x > (14/3) ∴ x ∈(-∞, (-4/3)) ∪((14/3), ∞) .

Q. Assertion $: ∣3 x - 5∣ > 9 \Rightarrow x \in (- \infty, \frac{- 4}{3}) \cup (\frac{14}{3}, \infty)$
Reason : The region containing all the solutions of an inequality is called the solution region.

Assertion is correct, reason is correct; reason is a correct explanation for assertion.

Assertion is correct, reason is correct; reason is not a correct explanation for assertion

Assertion is correct, reason is incorrect

Assertion is incorrect, reason is correct.

We have, $∣3 x - 5∣ > 9$
$\Rightarrow 3 x - 5 < - 9$ or $3 x - 5 > 9$
$\Rightarrow 3 x < - 4$ or $3 x > 14$
$\Rightarrow x < \frac{- 4}{3}$ or $x > \frac{14}{3}$
$∴ x \in (- \infty, \frac{- 4}{3}) \cup (\frac{14}{3}, \infty) .$

Q. Assertion :∣3x−5∣>9⇒x∈(−∞,3−4​)∪(314​,∞) Reason : The region containing all the solutions of an inequality is called the solution region.