Final answer:
Upon evaluating the expressions and calculating, none of the options (a. x=6, b. x = 8, c. x=10, d. x = 12) provided match the calculated value of x=8/3. There may be an error in the expressions or the listed answer options.
Step-by-step explanation:
The question requests us to find the value of x given that the mean of the expressions (3x+7), (x-9), (5x+11), and (6x-5) is 11. To find the mean, we add up all the expressions and divide by the number of expressions. This gives us:
((3x + 7) + (x - 9) + (5x + 11) + (6x - 5)) / 4 = 11
Combining like terms, we have:
(15x + 4) / 4 = 11
15x + 4 = 44
15x = 40
x = 40 / 15
x = 8/3 which is not a valid solution as it is not an option provided in the question. Therefore, another approach or correction is needed. The information provided does not directly help in solving this problem, thus there might be typos or misunderstandings in the original question formulation.