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 one solution: x=10.
The equation has one solution: x equals 10 .

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 infinite solutions.
The equation has infinite solutions.

1 answer

To solve for x, let's simplify the equation:

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

Next, let's combine like terms:
10x - 7x - 3x = 6 - 10
(10 - 7 - 3)x = - 4
0x = -4

Since 0 multiplied by any number is always 0, the equation becomes:
0 = -4

This is a contradiction because 0 cannot equal -4. Therefore, the equation has no solution.