Solve for x to determine if the equation has one, none, or infinite solutions.
5(2x+2)−7x=3x+6 (1 point)
Responses
The equation has one solution: x=6.
The equation has one solution: x equals 6 .
The equation has infinite solutions.
The equation has infinite solutions.
The equation has one solution: x=10.
The equation has one solution: x equals 10 .
The equation has no solution.
To solve the equation, we will start by simplifying both sides:
5(2x+2) - 7x = 3x + 6
10x + 10 - 7x = 3x + 6
3x + 10 = 3x + 6
Next, we can subtract 3x from both sides:
10 = 6
The equation simplifies to 10 = 6, which is false. Since this equation has no solution, the correct response is:
The equation has no solution.