Which of the following inequalities holds if 3.24 < x < 5.36?

Given the inequality in the question, we know that x is positive.
We can then quickly eliminate options A and D. This is because in both the options the value being added to x is itself greater than the value on the right and since x is positive the value of the LHS is only going to increase further.

Now, checking option B, we only need to check if the maximum possible value of LHS is less than 1.06 or not. The maximum possible value of LHS will be when x has the maximum possible value which is a little less than 5.36. If x = 5.36, LHS of Option B will be x - 4.3 = 5.36 - 4.3 = 1.06. Since the maximum possible value of x is a little less than 5.36, the value of LHS of option B will also be a little less than 1.06. Hence, option B will hold true.