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The given equation is \( x = \frac{y}{z} \). To determine the lower bound of \( x \), we need to consider how uncertainties in \( y \) and \( z \) affect the result. 

In interval arithmetic, if both \( y \) and \( z \) have known upper and lower bounds, the general rule for calculating the lower bound of a quotient \( x = \frac{y}{z} \) depends on the behavior of \( y \) and \( z \):

- To get the **lower bound** of \( x \), you would divide the lower bound of \( y \) by the upper bound of \( z \), assuming both values are positive. This is because dividing by a larger value results in a smaller outcome.

Thus, the correct answer to the question "how would you find the lower bound of \( x \)?" is:

\[
\frac{y_{\text{lower}}}{z_{\text{upper}}}
\]

This matches the second option in the list.

Would you like more details on how bounds work in such problems, or do you have any questions?

Here are 5 related questions:
1. How do you calculate the upper bound of \( x = \frac{y}{z} \)?
2. What happens to bounds if \( z \) can be negative?
3. How does interval arithmetic differ from standard arithmetic in uncertainty analysis?
4. Why is dividing by a larger number result in a lower value?
5. Can the lower bound of a product be calculated similarly to a quotient?

**Tip:** When calculating bounds, always be cautious of negative values, as they reverse the direction of inequalities.

Given that x = y/z, how would you find the lower bound of x?

Learn how to calculate the lower bound of the quotient x = y/z using interval arithmetic. This problem explores the mathematical concepts of bounds, algebra, and quotient rules, suitable for high school students in grades 10-12.

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