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=6.
The equation has one solution: x equals 6 .
The equation has one solution: x=10.
The equation has one solution: x equals 10 .
The equation has infinite solutions.
The equation has infinite solutions.
To solve the equation, first distribute 5 to 2x and 2:
10x + 10 - 7x = 3x + 6
Combine like terms:
3x + 10 = 3x + 6
Subtract 3x from both sides:
10 = 6
Since the equation leads to a false statement, there are no solutions. Therefore, the correct response is:
The equation has no solution.