Question

Match each point with the approximation of the irrational number given.



(4 points)
Point C
Point L
Point E
Point A
responses
3V--1100
n
V--20
1.3242526

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 are no solutions to the equation.
There are no solutions to the equation.

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

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.
There are infinitely many solutions to the equation.

The only solution to the equation is –6.

Answer 1

Let's address each part of your question step-by-step.

### Approximation of the Irrational Number
You listed several points and responses:

1. **Point C** -
2. **Point L** -
3. **Point E** -
4. **Point A** -

#### Responses:
- \(3\sqrt{2} \approx 4.24264\)
- \(n\) (not specified)
- \(\sqrt{20} \approx 4.47214\)
- \(1.3242526\)

Without specific numerical values corresponding to Points A, C, E, and L, I cannot accurately match each point to its approximation. If you provide me with the values for each point or clarify what each point numerically represents, I'd be happy to help match them correctly!

### Equation Analysis
Now, let's analyze the equation you provided:

The equation is:
\[
3x - 9x + 1 = 2(-3x + 1) - 1
\]

Simplifying the left side, we combine like terms:

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

Now simplifying the right side:

\[
2(-3x + 1) - 1 = -6x + 2 - 1 = -6x + 1
\]
This leads us to:
\[
-6x + 1 = -6x + 1
\]

### Conclusion
This statement \( -6x + 1 = -6x + 1 \) is always true, indicating that the equation holds for all values of \(x\). Therefore, the **correct response** based on this analysis is:

- **There are infinitely many solutions to the equation.**

If you need further assistance or additional information, feel free to ask!