To solve this problem, we need to determine the error interval for $x$ when the rounded value is 6.7 to one decimal place.

When a number is rounded to one decimal place, the possible values for $x$ are within a range where the rounded result remains 6.7. This range is defined by:

$6.65 \leq x < 6.75$

Here's the reasoning:

1. Lower Bound: If $x$ is 6.65, rounding it to one decimal place gives 6.7.
2. Upper Bound: If $x$ is 6.75, rounding it to one decimal place would result in 6.8.

Thus, the error interval for $x$ is: $6.65 \leq x < 6.75$

Would you like further details on this solution or any related topics?

Additional Questions:

1. What is an error interval, and why is it useful?
2. How would this interval change if rounding to two decimal places?
3. What happens to the interval if the rounded value is a whole number?
4. How do we determine rounding intervals for negative numbers?
5. What if the question asked for a rounded value of 6.8 instead?

Tip: Always check both the lower and upper bounds when calculating error intervals, especially in rounding-based questions.