SOLUTION: The results of a poll claiming a 4% margin of error indicated that a candidate was favored by 48% of the voters. Write an absolute value inequality representing the percent of vote

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Question 1170680: The results of a poll claiming a 4% margin of error indicated that a candidate was favored by 48% of the voters. Write an absolute value inequality representing the percent of voters favoring the candidate. Then solve the inequality to state the range of the candidate's support.
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break down this problem step by step.
**1. Define the Variable**
Let 'x' represent the actual percentage of voters favoring the candidate.
**2. Write the Absolute Value Inequality**
The margin of error (4%) means the actual percentage could be 4% higher or 4% lower than the poll result (48%). This can be represented as:
|x - 48| ≤ 4
**3. Solve the Absolute Value Inequality**
To solve the absolute value inequality, we need to consider two cases:
* **Case 1:** x - 48 ≤ 4
* Add 48 to both sides:
* x ≤ 52
* **Case 2:** -(x - 48) ≤ 4
* Multiply both sides by -1 (and reverse the inequality sign):
* x - 48 ≥ -4
* Add 48 to both sides:
* x ≥ 44
**4. State the Range of Candidate's Support**
Combining the two cases, we get:
44 ≤ x ≤ 52
**Therefore:**
* **Absolute Value Inequality:** |x - 48| ≤ 4
* **Range of Candidate's Support:** The candidate is favored by between 44% and 52% of the voters.