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The problem states that a company manufactures hand sanitizer bottles that are expected to contain 2.00 ounces of sanitizer, but the actual amount can differ by no more than 0.15 ounces from this expected amount. The task is to identify the inequality that models the unacceptable range for the amount, \( x \), of hand sanitizer.

### Step-by-step analysis:
1. **Expected value:** The expected amount is 2.00 ounces.
2. **Acceptable deviation:** The amount of sanitizer in the bottle can differ by no more than 0.15 ounces, meaning the difference between the actual amount, \( x \), and 2.00 should not exceed 0.15.
3. **Mathematical model:** The absolute difference between the actual amount, \( x \), and the expected amount, 2.00, should be less than or equal to 0.15.

This can be written as the inequality:
\[
|x - 2.00| \leq 0.15
\]
This inequality states that the actual amount of sanitizer can be at most 0.15 ounces more or less than 2.00 ounces. However, the question asks for the inequality that models the **unacceptable** range. This means we're looking for when the deviation is greater than 0.15.

Therefore, the inequality for the unacceptable range would be:
\[
|x - 2.00| > 0.15
\]

### Answer: The correct option is the one that shows \( |x - 2.00| > 0.15 \).

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Would you like more details or further clarification? Here are five related questions to deepen your understanding:

1. How can absolute value inequalities be solved step-by-step?
2. What does the solution \( |x - 2.00| \leq 0.15 \) look like on a number line?
3. How do you rewrite an absolute value inequality as two linear inequalities?
4. Why is absolute value used in this context, and how does it apply to real-world problems?
5. How can you determine the solution set for the unacceptable range inequality?

**Tip:** When dealing with absolute value inequalities, think of them as measuring the "distance" from a central value, in this case, 2.00 ounces.

Which inequality models the unacceptable range for the amount, x, of hand sanitizer in the bottle?

Learn how to model unacceptable ranges using absolute value inequalities for a hand sanitizer bottle expected to contain 2.00 ounces, with a tolerance of 0.15 ounces. Discover the inequality representing when the amount is outside the acceptable range.

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