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 negative 3 .

The equation has one solution: x=3
.

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. Simplifying gives: \[ 3x = 3x \]

Since both sides of the equation are equal, this means that the equation is true for all values of \(x\). Therefore, the equation has infinite solutions.

The correct response is:

• The equation has infinite solutions.