When Cynthia rounds a number $x$ to one decimal place, and the result is 6.7, we need to determine the range of values $x$ could have had before rounding, known as the error interval.

For a number rounded to one decimal place, it can vary by up to $\pm 0.05$ around the rounded value. Thus:

$6.7 - 0.05 = 6.65$ $6.7 + 0.05 = 6.75$

Therefore, the error interval for $x$ is:

$6.65 \leq x < 6.75$

Would you like further details or explanations on this process?

Here are some related questions you might find useful:

1. How does rounding affect the accuracy of data in real-world applications?
2. What would be the error interval if $x$ were rounded to two decimal places?
3. How do we calculate error intervals for whole numbers?
4. How can error intervals impact scientific calculations?
5. Why do we use inequalities for error intervals?

Tip: Always remember that the range for a rounded number extends equally in both directions from the rounded value.