To solve this problem, let's analyze the situation:

• Björn found that 27% of voters were likely to vote for the incumbent.
• The margin of error is 4%. This means the actual percentage of voters could vary by ±4% from 27%.

The possible percentage of voters that will vote for the incumbent could be between:

• Minimum percentage: $27 - 4 = 23\%$
• Maximum percentage: $27 + 4 = 31\%$

Now, let's look at each option to determine which correctly expresses this relationship:

1. A. $|27 - 4| = v$

   • This simplifies to $|23| = v$, which is incorrect. The minimum percentage is 23%, but this does not describe both the minimum and maximum.

2. B. $|v - 27| = 4$

   • This equation states that the absolute difference between $v$ and 27 is 4. This correctly captures both the lower and upper bounds, since $v$ can be either $27 - 4 = 23$ or $27 + 4 = 31$. This is correct.

3. C. $27 - v = 4$

   • This simplifies to $v = 23$, which only gives the minimum percentage but not the full range. This is incorrect.

4. D. $4 - v = 27$

   • This simplifies to $v = -23$, which is not meaningful in this context. This is incorrect.

5. E. $|4 - 27| = v$

   • This simplifies to $| -23 | = v$, or $v = 23$, which only describes the minimum percentage and not the maximum. This is incorrect.

6. F. $v - 4 = 27$

   • This simplifies to $v = 31$, which only gives the maximum percentage but not the full range. This is incorrect.

The correct answers are:

• B. $|v - 27| = 4$

Would you like further clarification on the concept?

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Here are five related questions to explore further:

1. How do you calculate the margin of error in a poll?
2. What is the significance of using absolute value equations in polls?
3. How does increasing the sample size affect the margin of error?
4. How is margin of error used in confidence intervals?
5. What other statistical methods are used in election polling?

Tip: When interpreting absolute value equations like $|x - a| = b$, remember they describe a distance of $b$ units from $a$ on a number line, accounting for both directions (positive and negative).