Final answer:
The puzzle involves converting numbers between different numerical bases. By solving the equation, we find that the base 'x' is 6. Therefore, the number 7 in base 6 is equivalent to the decimal number 7.Option B is the correct answer.
Step-by-step explanation:
The question provided is an algebraic puzzle in base arithmetic, in which we need to find the value of 'x' using the information given. The equation 11x = 112x-4 suggests that the number 11 in base 'x' is equal to the number 11 in base '2x - 4'. Since the number 11 in any base is the same as the base plus 1 (i.e., 10 + 1), we can write:
⇒x + 1 = 2x - 4 + 1
By simplifying the equation, we can solve for 'x':
⇒x = 6
Given that we have found the value of 'x', we can now find the value of 7x (which is the number 7 in base 'x' or, more specifically, base 6). The number 7 in base 6 is equivalent to 61 + 1, which is 7. Therefore, the value of 76 in decimal is 7.