Question 12.
All the values of x satisfying the inequality are
Question Explanation
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
Giving the boundary , hence giving us the valid range as
Region II:
In this case, the right-hand side will be a negative value, and hence, the sign would change when multiplying, giving the inequality
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 < x 8
Hence, Option B is the correct answer.
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