Final answer:
After analyzing the original equation (x + 2)/2 = y/5, we find that none of the provided statements a, b, or c correctly describe the relationship between x and y. However, the closest match, which is x/2 = (y - 5)/5, is not among the given options.
Step-by-step explanation:
If we have the equation (x + 2)/2 = y/5, we want to determine which of the provided statements must be true. To verify each option, we must manipulate the original equation algebraically. Let's examine statement a: x/2 = (y - 2)/5.
To test statement a, we first multiply both sides of our original equation by 5 to solve for y:
5 * ((x + 2)/2) = y
This gives us 5(x + 2) = 2y. Dividing both sides by 2 results in (5x + 10)/2 = y. Simplifying this yields (5x/2) + 5 = y.
If we solve this equation for x/2, we get:
x/2 = (y - 5)/5
This matches statement b, not statement a. Therefore, statement a is not correct.
Following a similar process, we can reject statement c, since (x+2)/5 = y/25 would imply multiplying both sides of the original equation by different factors, which is not a valid operation.
Through this process, we find that the correct statement that must be true based on the given original equation is b. x/2 = (y - 5)/5.