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 no solution.
The equation has no solution.

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 one solution: x=−3
.

Answer 1

To solve the equation \( 3(x + 2) - 6 = 3x \), we will first simplify the left side:

1. Distribute \( 3 \) on the left side:

\[ 3x + 6 - 6 = 3x \]

2. Simplify by combining like terms:

\[ 3x = 3x \]

Now, we see that both sides of the equation are equal, which means that this equation is always true, regardless of the value of \( x \).

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

The correct response is:

The equation has infinite solutions.