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
.

Answer 1

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

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

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

This equation simplifies to \( 3x = 3x \), which is true for all \( x \). This means that every value of \( x \) satisfies the equation.

Therefore, the equation has infinite solutions.

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