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 infinite solutions.
The equation has infinite solutions.

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

The equation has no solution.

Answer 1

To determine whether the equation has one, none, or infinite solutions, we need to solve for x:

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

This equation simplifies to 0 = 0, which is always true. This means that the equation has infinite solutions, as any value of x will satisfy the equation.

Therefore, the correct response is: The equation has infinite solutions.