Solve for x to determine if the equation has one, none, or infinite solutions.

Question

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 no solution.
The equation has no solution.

The equation has one solution: x=10.

Answer 1

To solve the equation:

5(2x+2) - 7x = 3x + 6
10x + 10 - 7x = 3x + 6
3x + 10 = 3x + 6
3x - 3x = 6 - 10
0 = -4

Since 0 does not equal -4, this indicates that there is no solution. Therefore, the correct response is:

The equation has no solution.