Final answer:
After distributing and combining like terms, the equation simplifies to 24 = -24, which is a contradiction and indicates that there are no real solutions to the equation. Therefore, the correct answer is C. The equation has no real solutions.
Step-by-step explanation:
The equation presented is 4(x + 6) + 7x = 11x - 24. To find the solution to this equation, we need to first simplify and solve for x. Let's solve it step by step:
- Distribute the 4 into the parenthesis: 4x + 24 + 7x = 11x - 24.
- Combine like terms on the left side: 11x + 24 = 11x - 24.
- Subtract 11x from both sides of the equation: 11x - 11x + 24 = 11x - 11x - 24 which simplifies to 24 = -24.
This last step yields a false statement, indicating that there are no real solutions to this equation because x has been eliminated and we are left with a contradiction. Thus, the correct answer is C. The equation has no real solutions.