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 no solution.
The equation has no solution.

The equation has one solution: x=10.

1 answer

To solve for x, we can simplify the equation first:

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

First, distribute the 5:

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

Combine like terms:

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

3x + 10 = 3x + 6

Now, subtract 3x from both sides:

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

10 = 6

Since this results in a false statement (10 is not equal to 6), there is no solution to this equation.

Therefore, the correct answer is:
The equation has no solution.