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 no solution.
The equation has no solution.
The equation has one solution: x=10.
The equation has one solution: x equals 10 .
The equation has one solution: x=6.
The equation has one solution: x equals 6 .
The equation has infinite solutions.
To solve for x, we will first distribute the 5 to (2x + 2) and the 6 to 1, and then combine like terms:
5(2x+2) - 7x = 3x + 6
10x + 10 - 7x = 3x + 6
3x + 10 = 3x + 6
Subtract 3x from both sides:
10 = 6
This statement is clearly false. Therefore, the equation has no solution.
The correct response is: The equation has no solution.