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

There are infinitely many solutions to the equation.

1 answer

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

  1. The original equation is:
    \( 3x - 9x + 1 = 2(-3x + 1) - 1 \)

  2. Simplifying the left side:
    \( 3x - 9x + 1 = -6x + 1 \)
    This is what we get after simplifying.

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

  4. Now we can equate both sides:
    \( -6x + 1 = -6x + 1 \)

At this point, we see that both sides of the equation are identical.

This implies that the equation is always true regardless of the value of \( x \). Therefore, there are infinitely many solutions to the equation, as every value of \( x \) satisfies it.

Correct Statement:
There are infinitely many solutions to the equation.