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The problem asks to calculate the **upper bound** for \( x \) in the equation \( x = 3y - 4z \), where:

- \( y = 940 \) (correct to 2 significant figures),
- \( z = 675 \) (correct to 3 significant figures).

### Step-by-Step Solution:

To find the **upper bound** for \( x \), we need to consider the highest possible values for \( y \) and \( z \) within their given precision.

1. **Upper bound of \( y \)**:
   - \( y = 940 \) (2 significant figures), so:
     \[
     \text{Upper bound of } y = 945
     \]
     This comes from \( 940 \) being rounded to the nearest 10, meaning \( y \) can be as large as \( 945 \).

2. **Upper bound of \( z \)**:
   - \( z = 675 \) (3 significant figures), so:
     \[
     \text{Upper bound of } z = 675.5
     \]
     This is because \( z \) can go up to \( 675.5 \), assuming the precision allows the rounding range from \( 675.0 \).

3. **Substitute into the equation**:
   Now, substitute the upper bounds of \( y \) and \( z \) into the equation \( x = 3y - 4z \):

   \[
   x = 3(945) - 4(675.5)
   \]

4. **Calculation**:
   \[
   x = 2835 - 2702 = 133
   \]

Thus, the **upper bound** for \( x \) is \( 133 \).

### Final Answer:
The upper bound for \( x \) is **133.000** (to 3 decimal places).

Would you like more details or further explanations on this?

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Here are 5 related questions to expand on the topic:

1. How would you calculate the lower bound for \( x \)?
2. What is the significance of significant figures in determining bounds?
3. How do you round numbers to a specific number of significant figures?
4. What is the difference between upper bounds and lower bounds in calculations?
5. How does uncertainty in measurements affect calculations like these?

**Tip**: Always round at the last step of the calculation to avoid rounding errors affecting the accuracy of your final result.

Work out the upper bound for the value of x, where y = 940 (correct to 2 significant figures) and z = 675 (correct to 3 significant figures).

Learn how to calculate the upper bound of x in the equation x = 3y - 4z where y = 940 and z = 675. This problem explains significant figures, algebraic manipulation, and bounds in measurements. Suitable for students in Grades 10-12.

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