Question
Look at the steps for solving the equation and choose a true statement.
3х - 9x + 1 =2(-3x+1)-1
6х + 1=-6x + 2 -1
6х + 1=-6x + 1
(1 point)
• The only solution to the equation is 1.
• The only solution to the equation is -6.
There is no way to know if there is a solution to this equation.
• There are infinitely many solutions to the equation.
• There are no solutions to the equation.
3х - 9x + 1 =2(-3x+1)-1
6х + 1=-6x + 2 -1
6х + 1=-6x + 1
(1 point)
• The only solution to the equation is 1.
• The only solution to the equation is -6.
There is no way to know if there is a solution to this equation.
• There are infinitely many solutions to the equation.
• There are no solutions to the equation.
Answers
Answered by
GPT-4o mini
Let's analyze the steps given to solve the equation and deduce the correct statement.
Starting from the original equation:
1. \( 3x - 9x + 1 = 2(-3x + 1) - 1 \)
Simplifying the left side:
\[
3x - 9x + 1 = -6x + 1
\]
Therefore, we have:
\[
-6x + 1 = -6x + 1
\]
Thus, we can rewrite the equation as follows:
\[
-6x + 1 = -6x + 1
\]
2. The next step leads to:
\[
6x + 1 = -6x + 2 - 1
\]
Simplifying the right side gives:
\[
6x + 1 = -6x + 1
\]
This simplifies to:
\[
6x + 1 = -6x + 1
\]
3. Rearranging leads us to:
\[
6x + 6x = 1 - 1
\]
Which simplifies to:
\[
12x = 0
\]
Therefore:
\[
x = 0
\]
Now we know \(x = 0\) is a solution to this equation.
Going back to the options provided:
- **The only solution to the equation is 1.** (False)
- **The only solution to the equation is -6.** (False)
- **There is no way to know if there is a solution to this equation.** (False)
- **There are infinitely many solutions to the equation.** (False)
- **There are no solutions to the equation.** (False)
Since we found \(x = 0\) as a solution, the correct conclusion based on the analysis and the information provided is that none of the choices listed are valid statements about the solutions to the equation; rather, the solution is \(x = 0\).
However, based on the options given, we can conclude that none of the statements are true. If you need a different analysis based on the constraints of just choosing from the provided options, please let me know!
Starting from the original equation:
1. \( 3x - 9x + 1 = 2(-3x + 1) - 1 \)
Simplifying the left side:
\[
3x - 9x + 1 = -6x + 1
\]
Therefore, we have:
\[
-6x + 1 = -6x + 1
\]
Thus, we can rewrite the equation as follows:
\[
-6x + 1 = -6x + 1
\]
2. The next step leads to:
\[
6x + 1 = -6x + 2 - 1
\]
Simplifying the right side gives:
\[
6x + 1 = -6x + 1
\]
This simplifies to:
\[
6x + 1 = -6x + 1
\]
3. Rearranging leads us to:
\[
6x + 6x = 1 - 1
\]
Which simplifies to:
\[
12x = 0
\]
Therefore:
\[
x = 0
\]
Now we know \(x = 0\) is a solution to this equation.
Going back to the options provided:
- **The only solution to the equation is 1.** (False)
- **The only solution to the equation is -6.** (False)
- **There is no way to know if there is a solution to this equation.** (False)
- **There are infinitely many solutions to the equation.** (False)
- **There are no solutions to the equation.** (False)
Since we found \(x = 0\) as a solution, the correct conclusion based on the analysis and the information provided is that none of the choices listed are valid statements about the solutions to the equation; rather, the solution is \(x = 0\).
However, based on the options given, we can conclude that none of the statements are true. If you need a different analysis based on the constraints of just choosing from the provided options, please let me know!