Question

A recent survey showed that the approval rating for the mayor of a particular town was 24% with a margin of error of +/-6%. Write an absolute value equation and solve it to find the range of approval percentage.

Answer 1

The range of approval percentage for the mayor is between 18% and 30%, based on solving the absolute value equation |x - 24| = 6, representing the approval rating with its margin of error.

Step-by-step explanation:

To find the range of approval percentage for the mayor with a given approval rating and margin of error, we can use an absolute value equation. The approval rating is 24% and the margin of error is ±6%. Therefore, the absolute value equation would be |x - 24| = 6. Solving this equation gives us two scenarios: x - 24 = 6 and x - 24 = -6. The solutions to these equations are x = 30 and x = 18, respectively.

This means that the range of approval percentage for the mayor can be estimated to be between 18% and 30%. The margin of error indicates the confidence interval within which the true approval rating is likely to fall.