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 infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=−3.
The equation has one solution: x equals negative 3 .

The equation has no solution.

Answer 1

Let's solve the equation step by step:

1. Start with the equation: \[ 3(x + 2) - 6 = 3x \]

2. Distribute the 3 on the left side: \[ 3x + 6 - 6 = 3x \]

3. Simplify the left side: \[ 3x = 3x \]

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

Since the equation holds true for all values of \(x\), we can conclude that:

• The equation has infinite solutions.

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