Look at the steps for solving the equation and choose a true statement.

Question

3x−9x+1=2(−3x+1)−1
−6x+1=−6x+2−1
−6x+1=−6x+1 (1 point)
Responses

There are infinitely many solutions to the equation.
There are infinitely many solutions to the equation.

The only solution to the equation is -6
The only solution to the equation is -6

There is no way to know if there is a solution to the equation.
There is no way to know if there is a solution to the equation.

The only solution to the equation is 1
The only solution to the equation is 1

There are no solutions to the equation.

Answer 1

Let's analyze the steps involved in the equation given.

Starting with:

\[ 3x - 9x + 1 = 2(-3x + 1) - 1 \]

The steps simplify as follows:

1. Combine like terms on the left side: \[ 3x - 9x + 1 = -6x + 1 \]

2. Expand the right side: \[ 2(-3x + 1) - 1 = -6x + 2 - 1 = -6x + 1 \]

So we have: \[ -6x + 1 = -6x + 1 \]

At this point, we see that both sides of the equation are identical:

\[ -6x + 1 = -6x + 1 \]

This implies that the equation is true for any value of \( x \).

Thus, the correct statement from the options provided is:

There are infinitely many solutions to the equation.