Question

2. 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 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 -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.

The only solution to the equation is 1
The only solution to the equation is 1

There are no solutions to the equatio

Answer 1

To analyze the steps provided in the equation:

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

2. Combine like terms on the left side:
\(-6x + 1 = 2(-3x + 1) - 1\).

3. On the right side, distribute and simplify:
\(-6x + 1 = -6x + 2 - 1\) which simplifies to \(-6x + 1 = -6x + 1\).

Now, you see that both sides of the equation are identical, which means:

\(-6x + 1 = -6x + 1\) is always true.

Thus, the true statement is:

There are infinitely many solutions to the equation.

This is because any value of \(x\) will satisfy the equation as it simplifies to a true statement.