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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 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.

1 answer

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

  1. Starting with the equation: \[ 3x - 9x + 1 = 2(-3x + 1) - 1 \] Simplifying the left side: \[ -6x + 1 = 2(-3x + 1) - 1 \]

  2. Expanding the right side: \[ -6x + 1 = -6x + 2 - 1 \] Which simplifies to: \[ -6x + 1 = -6x + 1 \]

At this point, both sides of the equation are equal: \[ -6x + 1 = -6x + 1 \]

This indicates that the original equation is always true for any value of \( x \). Therefore, there are infinitely many solutions to the equation.

Based on the choices provided, the true statement is: There are infinitely many solutions to the equation.