Final answer:
The second equation is not the result of a valid operation on the first equation. The equation 10 = 30(x - 3) suggests that only one side of the original equation was multiplied by (x - 3), which breaks the rules for maintaining equality.
Step-by-step explanation:
To determine if the second equation is the result of a valid operation on the first, we need to look at the principles of algebraic manipulation. When working with equations, multiplication or division by the same number on both sides of an equation preserves the equality. It's critical to ensure that the operation applies to every term on either side.
Given the first equation 10 = 30, we can multiply both sides by the same expression, (x - 3) in this case, to obtain a new equation. By doing so,
10 * (x - 3) = 30 * (x - 3)
This would simplify to:
10x - 30 = 30x - 90
However, the provided second equation is 10 = 30(x - 3), which implies only the right side of the first equation has been multiplied by (x - 3). This is not a valid operation as it does not apply the multiplication equitably to both sides, thus breaking the equality.