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 infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=3.

Answer 1

Let's solve the equation step by step:

The initial equation is: $$3(x+2)-6=3x$$

1. Distribute $3$ on the left side: $$3x+6-6=3x$$ $$3x=3x$$

2. Now, we simplify: $$3x=3x$$

This equation is always true for any value of $x$, meaning the left and right sides are identical.

Since we end up with $3x=3x$, which is true for any $x$, the equation has infinite solutions.

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