If x variable represents the money your brother has without the value of the airplane ticket, then, the expression x + 637 is the total money he has at the beggining.
In the sense of an inequality, it means x + 637 must be lower or equal than 2000 dollars, which was the initial money yoir brother had.
Then, you have:
x + 637 ≤ 2000
to solve the previous inequality, subtract 637 both sides:
x + 637 - 637 ≤ 2000 - 637 simplify both sides
x ≤ 1363
Hence, the solution to the ineuqality is x ≤ 1363
Your brother can spend at least 1363 dollars