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Question 1199963: A pollster reports that 58% of American favor a law that is pending in Congress. The error is less than 2%.
a. Write an absolute value inequality that describes the true percentage p of
American who are in favor of the legislation.
b. Solve your inequality in part a for p.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! **a) Write the absolute value inequality**
* Let 'p' represent the true percentage of Americans who favor the legislation.
* The error is less than 2%, meaning the difference between the reported percentage (58%) and the true percentage (p) is less than or equal to 2%.
* This can be expressed as:
|p - 58| ≤ 2
**b) Solve the inequality for p**
* **Case 1: p - 58 ≥ 0**
* p - 58 ≤ 2
* p ≤ 60
* **Case 2: p - 58 < 0**
* -(p - 58) ≤ 2
* -p + 58 ≤ 2
* -p ≤ -56
* p ≥ 56
* **Combine the solutions:**
* 56 ≤ p ≤ 60
**Therefore, the true percentage (p) of Americans who favor the legislation lies within the interval [56%, 60%].**
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