Question

a political polling agency predicts candidate a will win an election with 54% of the votes. their poll has a margin of error of 4% both above and below the predicted percentage. which inequality represents the predicted possible percent of votes, x, for candidate a?
options:
$52 \leq x \leq 56$
$x \geq 50$ or $x \leq 58$
$50 \leq x \leq 58$
$x \geq 52$ or $x \leq 56$

Explanation:

Step1: Understand the margin of error

The predicted percentage is 54% and the margin of error is 4% both above and below. So we need to find the range by subtracting and adding the margin of error to the predicted percentage.

Step2: Calculate the lower bound

Subtract the margin of error from the predicted percentage: $54 - 4 = 50$.

Step3: Calculate the upper bound

Add the margin of error to the predicted percentage: $54 + 4 = 58$.

Step4: Form the inequality

The possible percentage \( x \) should be between 50 and 58 (inclusive), so the inequality is \( 50 \leq x \leq 58 \).

Answer:

\( 50 \leq x \leq 58 \) (the third option: \( 50 \leq x \leq 58 \))