Solve for x

Question

to determine if the equation has one, none, or infinite solutions. 
3(x+2)−6=3x
(1 point)
Responses

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.
The equation has no solution.

The equation has one solution: x=−3
.

Answer 1

To solve the equation \(3(x + 2) - 6 = 3x\), we'll start by simplifying the left side of the equation:

1. Distribute \(3\) on the left side: \[ 3(x + 2) = 3x + 6 \] Therefore, the equation becomes: \[ 3x + 6 - 6 = 3x \] Simplifying further: \[ 3x = 3x \]

2. We see that both sides of the equation are equal. This means that the equation holds true for all values of \(x\).

Since the equation simplifies to a true statement ( \(3x = 3x\)), it has infinite solutions.

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