The solution set $\frac{3(x-2)}{7}≤\frac{5(x+4)}{9}, x \in R $ is :

$\left[-\frac{97}{4}, ∞\right)$

The correct answer is Option (3) → $\left[-\frac{97}{4}, ∞\right)$

$\frac{3(x-2)}{7}≤\frac{5(x+4)}{9}$

$⇒\frac{3(x-2)}{7}-\frac{5(x+4)}{9}≤0$

$⇒27(x-2)-35(x+4)≤0$

$⇒27x-35x-54-140≤0$

$⇒-8x-194≤0$

$⇒8x≥-194$

$⇒x≥-\frac{194}{8}=-\frac{97}{4}$