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

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

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

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 -6
The only solution to the equation is -6

There are no solutions to the equation.

Answer 1

Let's analyze the steps provided:

1. Original equation: \( 3x - 9x + 1 = 2(-3x + 1) - 1 \)
2. Simplified to: \( -6x + 1 = -6x + 2 - 1 \)
3. Further simplified to: \( -6x + 1 = -6x + 1 \)

The final statement \( -6x + 1 = -6x + 1 \) is true for all values of \( x \).

Because the equation simplifies to a true statement, it means that the original equation is an identity, which means there are infinitely many solutions.

Thus, the correct choice is:

There are infinitely many solutions to the equation.