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)ResponsesThe only solution to the equation is 1The only solution to the equation is 1There are infinitely many solutions to the equation.There are infinitely many 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 -6The only solution to the equation is -6There are no solutions to the equation.

Answer 1

Let's break down the steps for solving the given equation to determine which statement is true.

Initially, we have:

\[ 3x - 9x + 1 = 2(-3x + 1) - 1 \]

Simplifying the left side:

\[ 3x - 9x + 1 = -6x + 1 \]

Now simplifying the right side:

\[ 2(-3x + 1) - 1 = -6x + 2 - 1 = -6x + 1 \]

So now we have:

\[ -6x + 1 = -6x + 1 \]

Since both sides of the equation are identical, this indicates that any value of \( x \) will satisfy the equation. Therefore, the equation has infinitely many solutions.

So the correct statement is:

There are infinitely many solutions to the equation.