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Solve for x

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

The equation has infinite solutions.
The equation has infinite solutions.

The equation has one solution: x=3
.

1 answer

To solve the equation \(3(x + 2) - 6 = 3x\), follow these steps:

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

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

At this point, we can see that both sides of the equation are equal for any value of \(x\). This means that the equation does not depend on a specific value of \(x\), implying that there are infinite solutions.

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