Final answer:
The equation 17x - 42 = 6(2x-7) has one solution, which is x = 0.
Step-by-step explanation:
To determine the number of solutions for the equation 17x - 42 = 6(2x-7), we need to simplify and solve the equation. First, distribute 6 to the terms inside the parentheses: 17x - 42 = 12x - 42. Next, combine like terms by subtracting 12x from both sides: 17x - 12x - 42 = -42. Simplify further: 5x - 42 = -42. Finally, isolate x by adding 42 to both sides: 5x = 0. Therefore, the equation has one solution, x = 0.