Question

Solvefor 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 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 no solution.

Answer 1

Let's solve the equation step by step:

Given the equation:
\[ 3(x+2) - 6 = 3x \]

First, distribute \(3\) on the left side:
\[ 3x + 6 - 6 = 3x \]

Simplifying the left side:
\[ 3x + 6 - 6 = 3x \]
\[ 3x = 3x \]

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

Thus, the equation has **infinite solutions**.

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