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

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

Let's solve the equation step by step:

The initial equation is:
\[ 3(x + 2) - 6 = 3x \]

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

2. Now, we simplify:
\[ 3x = 3x \]

This equation is always true for any value of \( x \), meaning the left and right sides are identical.

Since we end up with \( 3x = 3x \), which is true for any \( x \), the equation has **infinite solutions**.

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