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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 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.

1 answer

To solve the equation \( 3(x + 2) - 6 = 3x \), we can start by simplifying the left side.

  1. Distribute \(3\) into \((x + 2)\): \[ 3x + 6 - 6 = 3x \]

  2. This simplifies to: \[ 3x = 3x \]

Now we can see that the equation \(3x = 3x\) holds true for all values of \(x\).

Since both sides are equal for any \(x\), this means that the equation has infinite solutions.

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