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.