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

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

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.

There are no solutions to the equation.

Answer 1

Let's analyze the steps given in solving the equation:

1. The original equation is: \( 3x - 9x + 1 = 2(-3x + 1) - 1 \).

2. After simplifying both sides, you arrive at: \( -6x + 1 = -6x + 2 - 1 \) which simplifies to \( -6x + 1 = -6x + 1 \).

Since both sides of the equation are equal (i.e., \( -6x + 1 = -6x + 1 \)), this means the equation holds true for all values of \( x \). Therefore, there are infinitely many solutions to the equation since the equation is an identity.

The true statement is:

There are infinitely many solutions to the equation.