Question

a recent poll suggests that 47% of american citizens are going to vote for the democratic candidate for president, with a margin of error of ±4.5%. what is an absolute - value inequality to determine the range of possible percentages the candidate could earn?
|x - 47| < 4.5
|x - 47| > 4.5
|x - 4.5| < 47
|x - 4.5| > 47

Explanation:

Step1: Understand margin - of - error concept

The true percentage $x$ is within a certain distance of the polled percentage.

Step2: Identify given values

The polled percentage is 47% and the margin of error is 4.5%.

Step3: Write absolute - value inequality

The distance between the true percentage $x$ and the polled percentage 47 is less than the margin of error 4.5. So the inequality is $|x - 47|<4.5$.

Answer:

A. $|x - 47|<4.5$