Question 466359
To prove it in a more concise way, start by saying that if c < d, we can add equal quantities to both sides to get another true inequality. If we add a to both sides, we get


a + c < a + d


We can also replace a with b, and vice versa, because a and b are equal. Replace the a on the RHS side with b to get


a + c < b + d


Done.