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 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

To solve the equation \( 3(x+2)−6=3x \), let's first simplify the left side:

1. Distribute \( 3 \) in the term \( 3(x + 2) \): \[ 3x + 6 - 6 = 3x \]
2. Combine like terms on the left: \[ 3x = 3x \]

Now, this results in the equation: \[ 3x = 3x \]

This is a true statement for all values of \( x \), meaning that any value of \( x \) will satisfy the equation. Therefore, the equation has infinite solutions.

The correct response is: The equation has infinite solutions.