How are the greater than, less than, and equal to symbols useful?

They are called relation symbols
they tell how something relates to something else

greater than tells ou that the the result must be more than, but not eqal to that numberd so example, we have to have something that flys higher than that bridge (100ft) but it cannot fly 100 or else it will crash

less than tells you that you must be less than, but not euqal to. example
 this thing must be less than 7 feet tall to fit under the doorway, it cannot be 7 feet or else it wont fit

equal to is an exact amount, nothing more or less
we have to have a screw that is this big, nothing more or less

less and greater than is nice since if you found a solution and you wanted to notate it, example
if the naswer is any number less than 10, it would be nicer to write x<10 instead of listing all numbers less than 10 since they could get very close example 9.999999999 forever
greater is the same, any number bigger than 30, you woul dhave to include 30.0000000001 and smaller which is hard, but with the x>30, it is easier

the equals just shows equality, this is equal to this, period