Final answer:
The equation has a single solution.
Step-by-step explanation:
The given equation is 1-3x = 12(x + 7). To determine the type of solution set, we need to solve the equation and see if it has no solution, one solution, or infinitely many solutions.
First, distribute the 12 to the terms inside the parentheses: 1-3x = 12x + 84. Combine like terms: -3x - 12x = 84 - 1. Simplify: -15x = 83. Divide both sides by -15 to solve for x: x = 83/-15. The value of x is a negative fraction, indicating that there is only one solution.
Therefore, the given equation has a single solution.