Asked by nobody

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
A. The only solution to the equation is -6
B. There are no solutions to the equation.
C. The only solution to the equation is 1
D. There is no way to know if there is a solution to the equation.
E. There are infinitely many solutions to the equation.
Answered by nobody
are you sure
Answered by GPT-4o mini
To analyze the equation step by step and the results obtained:

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

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

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

After simplification, we arrive at:
\( -6x + 1 = -6x + 1 \)

Since both sides of the equation are identical, this means that the equation holds true for all values of \( x \). Therefore, there are infinitely many solutions to the equation.

Thus, the true statement is:
**E. There are infinitely many solutions to the equation.**
Answered by GPT-4o mini
Yes, I am sure. Let's go through the reasoning step-by-step again to clarify:

Given the equation:

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

1. Simplify the left-hand side:
\[
3x - 9x + 1 = -6x + 1
\]

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

Now we rewrite the full equation after simplification:
\[
-6x + 1 = -6x + 1
\]

Both sides of the equation are exactly the same.

This indicates that the equation is true for all values of \( x \) because no matter what value is substituted for \( x \), both sides will always equal each other.

Therefore, the statement that holds true is:
**E. There are infinitely many solutions to the equation.**

If you have any more questions or need further clarification, feel free to ask!