Final answer:
Equation 1 has no solution, Equation 2 has one solution (x = 0), and Equation 3 has infinite solutions. The process involves simplifying and checking the reasonableness of the statements obtained.
Step-by-step explanation:
To determine whether the given equations have one, infinite, or no solutions, we will attempt to simplify each equation step by step.
Equation 1: 6x - 14 = 6x + 12
Subtract 6x from both sides:
-14 = 12
This statement is false, indicating that there are no solutions as it represents a contradiction.
Equation 2: 4x + 8 - 9x = 7 - 5x + 1
Combine like terms on each side:
4x - 9x + 5x = 7 + 1 - 8
-4x = 0
Divide by -4:
x = 0
This equation has exactly one solution, which is x = 0.
Equation 3: 2x + 9 = 2x + 3 + 6
Combine like terms on the right side: 2x + 9 = 2x + 9
Subtract 2x from both sides:
9 = 9
This statement is true for all values of x, indicating that there are infinite solutions.
When solving such equations, it is crucial to eliminate terms wherever possible and to check if the resulting statements are reasonable.