Solve for x to determine if the equation has one, none, or infinite solutions.

Question

3(x+2)−6=3x(1 point)
Responses

The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .

The equation has one solution: x=3.
The equation has one solution: x equals 3 .

The equation has infinite solutions.
The equation has infinite solutions.

The equation has no solution.
The equation has no solution.

Answer 1

To solve the equation 3(x+2)−6=3x, we can start by simplifying both sides of the equation:

3(x+2)−6 = 3x
3x + 6 - 6 = 3x
3x = 3x

We can observe that the variable, x, is present on both sides of the equation and the terms cancel each other out. This means that the equation has an infinite number of solutions.

So the correct response is:
The equation has infinite solutions.