Question 12.

There are two critical points for the inequality to consider: x=-5 and x=3/2

Region I: x is greater than 3/2

In this scenario, both the terms would be positive; cross-multiplying, we get the relation $2x-3\le x+5$

Giving the boundary $x\le8$, hence giving us the valid range as $\frac{3}{2} \lt x \leq 8$

Region II: $-5 \lt x \lt \frac32$

In this case, the right-hand side will be a negative value, and hence, the sign would change when multiplying, giving the inequality

$2x-3\ge x+5$

Which will give x>8, which is out of bounds for this region 

Another way is to put a value in the region to check for the validity of the inequality; by putting x=0, we could see that the inequality does not hold in this region 

Region III: x less than -5

In this scenario, both the terms are negative, essentially giving us the same boundary as region 1; we take the lower bounds, giving us that x has to be less than 5

Therefore, for the given inequality to hold true x<-5 or $\frac{3}{2}$ < x $\le$ 8

Hence, Option B is the correct answer.