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The given problem asks to estimate one solution to the nearest tenth for the equation:

\[
-2x + 9 = 5^x
\]

You are provided with a table of values that shows the left-hand side (`-2x + 9`) and the right-hand side (`5^x`) of the equation for different values of \(x\). The goal is to find where these two expressions are approximately equal.

### Table Values
| \(x\)   | \(-2x + 9\) | \(5^x\) |
|--------|-------------|--------|
| 0      | 9           | 1      |
| 1      | 7           | 5      |
| 2      | 5           | 25     |
| 1.1    | 6.8         | 5.9    |
| 1.2    | 6.6         | 6.9    |
| 1.15   | 6.7         | 6.4    |

### Finding the Solution
We need to find an \(x\) where the values of \(-2x + 9\) and \(5^x\) are approximately the same. By inspecting the table, we see that the values for \(x = 1.15\) are:

- \(-2(1.15) + 9 = 6.7\)
- \(5^{1.15} = 6.4\)

These values are very close to each other, suggesting that \(x = 1.15\) is an approximate solution to the equation.

### Conclusion
The estimated solution to the equation is:
\[
x \approx 1.15
\]

Would you like further details or have any questions?

Here are five related questions you might explore:
1. How does the value of \(5^x\) behave as \(x\) increases?
2. How can we improve our estimate of \(x\) to be even more precise?
3. Can we use a graph to visually find the solution of the equation?
4. What method can be used to solve this equation algebraically?
5. How does rounding affect the accuracy of our estimate?

**Tip**: When approximating solutions using tables or graphs, it's important to consider interpolation between values to refine your estimate.

Use the table to estimate one solution, to the nearest tenth, of this equation: -2x + 9 = 5^x.

Learn how to estimate the solution to the equation -2x + 9 = 5^x using a table of values. This problem explores algebraic concepts and exponential functions, with step-by-step analysis on finding an approximate solution.

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