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 no solution.
The equation has no solution.

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

The equation has infinite solutions.

Answer 1

To solve the equation \( 3(x + 2) - 6 = 3x \), let's first simplify it step by step.

1. Distribute the \( 3 \) on the left side:

\[ 3(x + 2) = 3x + 6 \]

So, the equation becomes:

\[ 3x + 6 - 6 = 3x \]

2. Simplify the left side:

\[ 3x + 6 - 6 = 3x \implies 3x = 3x \]

Since both sides of the equation are the same, this means the equation is true for all values of \( x \).

Thus, the equation has infinite solutions.

Conclusion:

The correct response is: "The equation has infinite solutions."