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 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

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

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

There are no solutions to the equation.

Answer 1

Let's analyze the steps provided for solving the equation:

1. Starting with the original equation: \[ 3x - 9x + 1 = 2(-3x + 1) - 1 \]

2. Simplifying both sides leads to: \[ -6x + 1 = -6x + 2 - 1 \]

3. Simplifying the right-hand side: \[ -6x + 1 = -6x + 1 \]

At this point, we have the equation: \[ -6x + 1 = -6x + 1 \]

This indicates that both sides of the equation are identical. This means that any value for \(x\) will satisfy the equation. Therefore, the correct statement is:

There are infinitely many solutions to the equation.