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 infinite solutions.
The equation has infinite solutions.

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 distributing the 5 to the terms inside the parentheses:

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

Next, combine like terms on both sides of the equation:

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

Simplifying further:

0 = -4

Since we have reached a contradiction (0 does not equal -4), there is no solution to the equation. Thus, the correct response is:

The equation has no solution.