Question

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
.

Answer 1

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.**