Final answer:
The solutions to the equation 15(2a - 2) = 5(c² - 1) do not directly correspond to the answer choices provided. By simplifying the equation, we find that a equals (c² + 5) / 6, indicating that for each real number value of c, there is a unique corresponding value of a.
Step-by-step explanation:
The student's question involves solving an equation using cross-multiplication. To find the solutions to the equation 15(2a - 2) = 5(c² – 1), we can first simplify both sides by dividing by 5, which is a common factor. This gives us 3(2a - 2) = c² – 1. We can further simplify it by expanding the brackets to obtain 6a - 6 = c² – 1. Adding 6 to both sides gives us 6a = c² – 1 + 6, which simplifies to 6a = c² + 5. Finally, dividing both sides by 6 yields a = (c² + 5) / 6. This equation shows the relationship between a and c, and since there's no contradiction, it doesn't match with any of the given answer choices directly. If c is any real number, a will be a unique corresponding value following this formula. Therefore, we cannot select an option from a), b), c), or d) based solely on the information given in the equation.