Question

Statement-I: $ |3x - 5| > 9 \Rightarrow x \in\left(-\infty,\, \frac{-4}{3}\right) \cup \left(\frac{14}{3}, \,\infty\right)$.
Statement-II: The region containing all the solutions of an inequality is called the solution region.

• A. If both Statement-I and Statement-II are true and Statement-II is the correct explanation of Statement-I
• B. If both Statement-I and Statement-II are true but Statement-II is not the correct explanation of Statement-I
• C. If Statement-I is true but Statement-II is false
• D. If Statement-I is false and Statement-II is true

Answer 1

Answer: (B)

We have, $|3x - 5| > 9$
$\Rightarrow \quad3 x -5 < -9 \quad$ or $\quad 3 x -5> 9$
$\Rightarrow \quad 3x < - 4 \quad$ or $\quad 3x > 14$
$\Rightarrow \quad x < \frac{-4}{3}\quad$ or $\quad x > \frac{14}{3}\quad\therefore \quad x \in\left(-\infty,\, \frac{-4}{3}\right) \cup \left(\frac{14}{3}, \,\infty\right)$