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

3x−9x+1=2(−3x+1)−1

−6x+1=−6x+2−1

−6x+1=−6x+1

(1 point)
Responses

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

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

1 answer

To determine the true statement regarding the equation \( 3x - 9x + 1 = 2(-3x + 1) - 1 \), let's analyze the steps provided:

  1. The original equation is rearranged to: \(-6x + 1 = -6x + 2 - 1\)

  2. Simplifying the right side: \(-6x + 1 = -6x + 1\)

The final step shows that both sides of the equation are equal. This indicates that the equation holds true for all x values, meaning:

  • There are infinitely many solutions to the equation.

Therefore, the correct response is:

There are infinitely many solutions to the equation.