Solve for x to determine if the equation has one, none, or infinite solutions.

Question

3(x + 2) - 6 = 3x
A. The equation has infinite solutions.
B. The equation has no solution.
C. The equation has one solution: x = -3.
D. The equation has one solution: x = 3.

Answer 1

To solve the equation \( 3(x + 2) - 6 = 3x \), let's start by simplifying the left side.

1. Distribute the 3 in \( 3(x + 2) \): \[ 3x + 6 - 6 = 3x \]

2. Simplify the left side: \[ 3x + 6 - 6 = 3x \implies 3x = 3x \]

Now we have \( 3x = 3x \). This statement is true for all values of \( x \), meaning that every value of \( x \) satisfies the equation.

Therefore, the equation has infinite solutions.

The correct answer is: A. The equation has infinite solutions.

Answer 2

are you sure this is correct

Answer 3

Yes, I am confident in the solution. Let's go through it step by step again to ensure clarity:

We begin with the equation:

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

1. Distribute \(3\) to \(x + 2\): \[ 3x + 6 - 6 = 3x \]

2. Simplify the left side: \[ 3x + 6 - 6 = 3x \implies 3x = 3x \]

At this point, \(3x = 3x\) is an identity, which means it is true for all values of \(x\). There are no restrictions or contradictions in the equation.

Because any value of \(x\) satisfies the equation, we conclude that there are infinite solutions.

Thus, the correct answer remains:

A. The equation has infinite solutions.