Write an equation involving absolute value that can be used to find the maximum and minimum possible weight for a bag of the cat food. Let  represent the maximum or minimum weight of a bag of food.

To find the maximum and minimum possible weight of a bag of cat food, we can use an absolute value equation. Suppose the nominal weight of the bag is \( w_0 \) (the expected or advertised weight), and the actual weight \( w \) can vary by a certain amount \( \delta \) (which represents the possible deviation from the nominal weight).

The equation to find the maximum and minimum possible weight of the bag can be written as:

\[
|w - w_0| = \delta
\]

Here, \( w \) represents the actual weight, \( w_0 \) is the nominal weight, and \( \delta \) is the allowed deviation from \( w_0 \).

### Explanation:
- The absolute value \( |w - w_0| \) ensures that the difference between the actual weight \( w \) and the nominal weight \( w_0 \) is within the allowed range \( \delta \).
- This equation means that the actual weight \( w \) can be either \( w_0 + \delta \) (the maximum weight) or \( w_0 - \delta \) (the minimum weight).

### Example:
If the nominal weight \( w_0 \) is 10 kg and the allowed deviation \( \delta \) is 0.5 kg, the equation becomes:

\[
|w - 10| = 0.5
\]

This gives us the possible weights \( w = 10.5 \) kg (maximum) or \( w = 9.5 \) kg (minimum).

Would you like more details or have any questions?

### Related Questions:
1. How can we solve the absolute value equation for the weight?
2. What happens if the deviation \( \delta \) is 0?
3. How can this method be applied to find the weight range of multiple bags?
4. Can this approach be used for finding weights if the deviation \( \delta \) is different for each bag?
5. What are other real-world examples where absolute value equations are useful?

### Tip:
Always double-check units when working with weights, especially when calculating deviations, to ensure accuracy in measurements.

Learn how to use absolute value equations to determine the maximum and minimum possible weight of a bag of cat food. Understand the concept of nominal weight, actual weight, and allowed deviation in this mathematical problem-solving scenario.

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