Final answer:
The equation 4.12x + 5.2 = 8.23, when scaled by a factor of 100, becomes 412x + 520 = 823, making option (2) the equivalent equation.
Step-by-step explanation:
The equation 4.12x + 5.2 = 8.23 is best transformed into an equivalent equation by scaling all terms by a factor of 100. To maintain the equality, each term on both sides of the equation must be multiplied by the same factor. Multiplying by 100 transforms the equation into 412x + 520 = 823, which corresponds to option (2). It's important to note that multiplying by 100 removes the decimals without changing the proportion between the terms.
To algebraically rearrange equations, like dividing 0.40 into both sides or multiplying both sides by a certain factor, is critical for maintaining equivalent expressions. The process of scaling is used in linear equations to simplify calculations without affecting the solution set of the equation.