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The problem asks which equation represents the limits of the width, \( w \), of the packing material, given that the packing material's width should be within 0.8 mm of the desired thickness, which is 18.0 mm.

The key point here is that the width of the material can vary by at most 0.8 mm from the desired width of 18.0 mm. This situation can be modeled with an absolute value inequality:

\[
| w - 18.0 | \leq 0.8
\]

This inequality expresses that the difference between the actual width \( w \) and the desired width of 18.0 mm should be at most 0.8 mm. Simplifying or writing the equation for this in a different form will help us match it to one of the choices.

Now let's analyze the options:

- **Option A: \(|0.8 - w| = 18.0\)**  
  This does not represent the situation correctly, since the difference between \( w \) and the target value (18.0) should be no more than 0.8, not the reverse.

- **Option B: \(|18.0 - w| = 0.8\)**  
  This is a correct equation. It says that the absolute difference between the desired thickness (18.0 mm) and the actual width \( w \) is exactly 0.8 mm.

- **Option C: \(|18.0 + w| = 0.8\)**  
  This doesn't make sense because adding \( w \) to 18.0 isn't relevant to the problem.

- **Option D: \(|0.8 + w| = 18.0\)**  
  Again, this doesn't match the situation as we are not summing \( w \) and 0.8.

Thus, **the correct answer is B: \(|18.0 - w| = 0.8\)**.

Would you like more details on the reasoning behind the inequality? Here are some related questions to consider:

1. How do absolute value equations help in defining a range of values?
2. What would be the solution set for \(|18.0 - w| = 0.8\)?
3. How can this type of inequality be applied in other real-world scenarios?
4. How do you interpret absolute value equations graphically?
5. What are other ways to represent deviations from a target value?

**Tip:** When working with absolute value equations, always remember that it expresses the distance between two values.

Estefani is designing the manufacturing that will produce packing material for a particular computer chip. The packing material needs to be within 0.8 mm of the desired thickness, which is 18.0 mm. Which equation can Estefani use to represent the limits of the width, w, of the packing material?

Learn how to use absolute value inequalities to represent the limits of the width of a packing material for a computer chip. The packing material's width must be within 0.8 mm of the desired thickness, which is 18.0 mm. Suitable for students in Grades 8-10.

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