Final answer:
Based on the importance of simplifying an equation, Paul's first step in solving the equation 2x^3 - 49 = 5(x + 1)^6 + 4 appears to be more effective as it aimed at simplification. Without specific details, it's assumed that simplification without error is the better approach.
Step-by-step explanation:
In addressing who took the better first step in solving the equation 2x^3 - 49 = 5(x + 1)^6 + 4, we need to look for simplification and correct mathematical manipulation as primary indicators of an effective strategy. Theresa and Paul's first steps are not explicitly provided in the question, but based the given options and supporting information, it's important to eliminate terms and simplify the equation as much as possible to reach a solution. The reference to simplifying the denominator and recognizing a perfect square suggests that correctly reducing the equation to its simplest form, while keeping it accurate, is the key to determining which first step is better.
Paul's step, characterized by 'simplifying the left side of the equation', aligns with our aim of simplification. This could indicate that he has indeed simplified the equation, which is typically considered a strong first step in problem-solving. Without explicit details on Theresa's first step, but given the clues that no common denominator is necessary in this context and incorrectly multiplying by a factor would be an error, the choice between these two seems to point towards Paul's approach as likely being more effective.
Thus, if we had to choose based on these reasons, we would select Option 2: Paul took the better first step because he simplified the left side of the equation. However, without the specific details of their steps, this answer is based on the understanding that simplifying an equation generally makes it easier to solve, as long as the steps taken are mathematically correct.