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

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.
The equation has infinite solutions.

1 answer

To solve the equation, we can start by distributing the 3 to both terms inside the parentheses:

3x + 6 - 6 = 3x

Simplifying, we get:

3x = 3x

Now, we can subtract 3x from both sides of the equation:

3x - 3x = 0

Simplifying further, we get:

0 = 0

Since this equation is always true, it means that any value of x will satisfy the equation. Therefore, the equation has infinite solutions.