Final answer:
The student's question contains a typo and does not present a valid mathematical inequality. Solving a similar inequality involving an absolute value would yield a solution of x > 25/2. For the probability question, the conditional probability is calculated using the formula P(A given B) = P(A and B) / P(B), but without additional information, we cannot provide an exact answer.
Step-by-step explanation:
The student's question appears to have a typo but seems to be asking for the solution to an inequality that potentially involves an absolute value, given the brackets. However, no operation (like greater than or less than) is given between the repeated expression [2x−7] and 11, so the provided inequality does not make sense as written. Despite the misunderstanding, let's approach a similar problem that makes more sense mathematically:
Let's say we have [2x-7] > 11. To solve it, we would first isolate the absolute value expression by adding 7 to both sides of the inequality:
- |2x-7| > 18
- Next, we solve the inequality for 2x-7 being both greater than 18 and less than -18.
- For 2x-7 > 18, we get x > 25/2.
- For 2x-7 < -18, no solution exists because an absolute value cannot be negative.
- Thus, the solution to the modified inequality would be x > 25/2.
Regarding probability, if we want to find P(x>12| x>8), we would need to consider that this is a conditional probability, which is calculated as the probability of A happening given that B has occurred. Using the provided information in the question:
- P(A given B) = P(A and B) / P(B)
- Given A is (x > 12) and B is (x > 8), we would calculate the joint probability P(A and B) and then divide it by P(B).
However, without more context or a specified probability distribution, we cannot calculate this probability precisely.