2. 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 1
The only solution to the equation is 1

There are no solutions to the equation.
There are no 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.

Answer 1

To solve the equation step-by-step:

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

2. Simplify the left side: \[ 3x - 9x + 1 = -6x + 1 \]

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

4. You now have: \[ -6x + 1 = -6x + 1 \]

This means both sides of the equation are identical for any value of \(x\). Therefore, the equation holds true for all \(x\).

Consequently, the correct statement is: There are infinitely many solutions to the equation.