Final answer:
The absolute value inequality representing my approval rating as a class president is |x - 78| ≤ 3; therefore, my approval rating falls between 75% and 81%.
Step-by-step explanation:
This absolute value inequality, |x - 78| ≤ 3, reflects the margin of error (±3%) around the observed approval rating (78%). Breaking it down, the inequality states that the difference between my approval rating (x) and the observed 78% should be within 3 percentage points.
The absolute value ensures both the positive and negative deviations within the margin of error are considered. Solving it reveals the range within which my actual approval rating lies: subtracting and adding 3 from the observed 78% gives the lower limit of 75% (78% - 3%) and the upper limit of 81% (78% + 3%).
So, my actual approval rating as a class president is between 75% and 81%.
Correct answer: [x-78]<3;75%<x_<81%
Complete question:
- In a poll of 100 people, you have an approval rating as a class president of 78% with a 3% margin of error. Write and solve an absolute value inequality that represents your approval rating.