Final answer:
The student's question revolves around preferred methods for solving an algebraic equation, highlighting two different approaches: division first and applying the Distributive Property first. Both methods are correct and lead to the same result, with personal preference and ease of understanding being the determining factors for which one to use.
Step-by-step explanation:
The student is asking which method is preferable for solving the equation -24 = 5(g + 3). One method is to divide each side by 5 before solving for g, and the other is to use the Distributive Property to first eliminate the parentheses and then solve for g. Both methods are valid, and preference can depend on the individual.
Using the Distributive Property, you would multiply 5 by both g and 3, getting -24 = 5g + 15, and then subtracting 15 from both sides to get -39 = 5g, followed by dividing by 5 to isolate g. Alternatively, dividing each side by 5 initially gives -4.8 = g + 3, and then subtracting 3 from both sides yields -7.8 = g.
Both approaches ultimately provide the correct value of g, but some students may find one method easier to understand or perform in the head than the other. From a teaching perspective, it's beneficial to show both methods to demonstrate that mathematics can provide multiple paths to the same answer.