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 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.

1 answer

To solve for x, we can start by simplifying the equation:

5(2x+2) - 7x = 3x + 6

Distribute the 5:

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

Combine like terms:

3x + 10 = 3x + 6

Subtract 3x from both sides:

10 = 6

This is a contradiction, as 10 cannot equal 6. Therefore, the equation has no solution.