In this case, the poll indicates that the leading candidate is projected to receive 52% of the votes, but there is a margin of error of ±3%. The margin of error accounts for potential variation between the sample data (the poll results) and the true percentage of votes the candidate might receive.

Let $x$ represent the true percentage of votes received by this candidate.

The true percentage $x$ will fall within the range:

$52\% - 3\% \leq x \leq 52\% + 3\%$

Simplifying:

$49\% \leq x \leq 55\%$

Thus, the true percentage of votes $x$ for the candidate is between 49% and 55%, accounting for the margin of error.

Let me know if you'd like more details or have any questions! Here are some related questions:

1. What is the significance of the margin of error in political polling?
2. How would the margin of error change if the sample size were increased?
3. What statistical methods are used to calculate the margin of error in a poll?
4. If the margin of error were 5%, how would the range of $x$ change?
5. How does a margin of error of ±3% affect the interpretation of a candidate's support?

Tip: When interpreting polling results, always consider the margin of error to understand the potential variability in the true outcome!