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 infinite solutions.
The equation has infinite solutions.
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 no solution.

1 answer

To solve the equation, first distribute the 5 on the left side:

10x + 10 - 7x = 3x + 6

Combine like terms:

3x + 10 = 3x + 6

Subtract 3x from both sides:

10 = 6

This equation is a contradiction, so there are no solutions. Therefore, the correct response is:

The equation has no solution.