Final Answer:
The option that does not correspond to the equation a + 3b = 5c - 9 is (b) a + 3b + 9.
Step-by-step explanation:
The original equation is a + 3b = 5c - 9. To find the expression not equivalent to this equation, let's analyze the options. Option (b) a + 3b + 9 can be simplified:
a + 3b + 9 is not equivalent to a + 3b = 5c - 9 because adding 9 to the left side changes the equation's balance and alters its structure. In the original equation, 5c is present on the right side, but adding 9 to the left side introduces an inconsistency with the constant term.
Regarding the other options:
a) a = 50 - 9 - 3b: This equation can be rearranged to a + 3b = 50 - 9, which simplifies to a + 3b = 41, not equivalent to the original equation.
c) 5 = 50 - 9 - a: When rearranged, this becomes a = 50 - 9 - 5, which simplifies to a = 36. This doesn't match the original equation a + 3b = 5c - 9.
d) 3 = b + 1: This equation is unrelated to the original equation a + 3b = 5c - 9 and represents a relationship between b and 3, which doesn't correspond to the original structure.
Thus, by the process of elimination and evaluating each option against the original equation a + 3b = 5c - 9, it is evident that (b) a + 3b + 9 is not equivalent to the given equation due to the addition of 9 altering the equation's balance and structure.