Question

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

The only solution to the equation is -6
There is no way to know if there is a solution to this equation
The only solution to the equation is 1
There are no solutions to the equation
There are infinitely many solutions to the equation

Answer 1

Let's analyze the steps you provided for solving the equation step-by-step:

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

2. Simplify the left side:
\( -6x + 1 \)

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

Now we have:
\( -6x + 1 = -6x + 1 \)

This simplifies to an identity since both sides are equal for all values of \( x \). Therefore, there are infinitely many solutions.

Based on this analysis, the correct statement is:

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