Question

Public opinion polls reported in newspapers are usually given with a margin of error. A poll for a local election determined that Candidate Morrison will receive 51% of the votes. The stated margin of error is +3%.

a. Write and solve an absolute value equation that represents the problem.
b. Solve the equation to find the minimum and maximum percent of the vote that Candidate Morrison can expect to receive.

Answer 1

An absolute value equation representing the range of votes Candidate Morrison can receive is |x - 51| = 3. Solving this equation gives us a minimum of 48% and a maximum of 54% for the actual percentage of votes Morrison could receive, considering the ±3% margin of error.

Step-by-step explanation:

To solve this problem, we need to understand that the margin of error operates in both directions from the given percentage point of the poll result. Given that Candidate Morrison is projected to receive 51% of the votes with a margin of error of ±3%, we can write an absolute value equation that represents the range of possible outcomes for the actual percentage of votes Morrison could receive.

The absolute value equation is:

|x - 51| = 3

This equation tells us that the difference between the actual percentage of votes, x, and the reported 51% can be at most 3%, regardless of direction. We solve it by considering both the positive and negative scenarios:

• x - 51 = 3 leads to x = 54
• x - 51 = -3 leads to x = 48

Therefore, the minimum and maximum percent of the vote that Candidate Morrison can expect to receive is 48% and 54%, respectively.