Question

Solve for x to determine if the equation has one, none, or infinite solutions. 3(x+2)−6=3x (1 point)ResponsesThe 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.The equation has no solution.The equation has one solution: x=3.

Answer 1

Let's solve the equation step-by-step:

The equation is:

\[ 3(x + 2) - 6 = 3x \]

First, distribute the 3 on the left side:

\[ 3x + 6 - 6 = 3x \]

This simplifies to:

\[ 3x = 3x \]

Now, we see that both sides of the equation are equal for any value of \( x \). This means that the equation is true for all values of \( x \).

Therefore, the equation has infinite solutions.

So, the correct response is:

The equation has infinite solutions.