\begin{tabular}{l}2.3 Suppose \( x \) represents the unit of calculating the resale value of the plot in millions of rands. \\ Which of the following values of \( x \) gives the best value of the plot? Substantiate your answer \\ with appropriate calculations. \\ \( \qquad \begin{array}{l}x=2 \\ x=5 \\ x=-3\end{array} \) \\ Conclusion: \\ \hline\end{tabular}
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Beyond the Answer
When calculating the resale value of a plot in millions of rands, higher values of \( x \) typically indicate a greater potential value. Between the given options, \( x = 5 \) stands out as the best value, assuming the value is based on historical data and market trends that support higher prices for properties priced in that range. For instance, if we calculate a hypothetical resale value using a formula such as \( Value = Base + (x \times Multiplier) \), selecting \( x = 5 \) would yield a greater resultant resale value compared to \( x = 2 \) or \( x = -3 \), which could indicate negative value or debt. To substantiate this mathematically, let’s say the base resale value is 1 million rands and the multiplier is 1 million rands for every unit. Thus, for \( x = 2 \), the value would be \( 1 + (2 \times 1) = 3 \) million rands; for \( x = 5 \), it would be \( 1 + (5 \times 1) = 6 \) million rands; and for \( x = -3 \), it would be \( 1 + (-3 \times 1) = -2 \) million rands. Clearly, the optimal resale value is achieved with \( x = 5 \), leading to a conclusion that maximizing \( x \) yields the best financial outcome in this scenario.
