Question

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 3 . The equation has infinite solutions. The equation has infinite solutions. The equation has one solution: x=−3.

Answer 1

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

1. Distribute the 3:
\[
3(x+2) = 3x + 6
\]
Thus, the equation becomes:
\[
3x + 6 - 6 = 3x
\]

2. Simplifying gives:
\[
3x = 3x
\]

This shows that both sides of the equation are equal for all values of \( x \). Therefore, we have an identity, and this means that there are infinite solutions.

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