How do you define a variable and write an algebraic expression for the phrase: 3 increased by a number?
Depends on context:
Let the variable be ...... ( what ever you chose)
This variable could have definable limits or belong to a particular set of number types
You could say "There exists a number n such that .....
or you could write:
On the simpler context
Let the variable be n such that
n would have to be positive otherwise it would not "increase" 3 when added.