$-\dfrac{3}{2} \le -\dfrac{2x}{3}$ where x ∈ R.

Assertion (A): The largest value of x is $\dfrac{9}{4}$.

Reason (R): When the signs of both the sides of an inequalities are changed, the sign of inequality reverses.

1. A is true, R is false.

2. A is false, R is true.

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

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

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

Reason

According to the assertion:

$\Rightarrow -\dfrac{3}{2} \le -\dfrac{2x}{3}\\[1em] \Rightarrow \dfrac{3}{2} \ge \dfrac{2x}{3}\\[1em] \Rightarrow x \le \dfrac{3 \times 3}{2 \times 2}\\[1em] \Rightarrow x \le \dfrac{9}{4}$

So, Assertion (A) is true.

According to the reason:

When you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign must be reversed to maintain the validity of the inequality

So, Reason (R) is true.

Hence, option 3 is correct.