The inequality x<5 is a statement about the size of x compared to 5 

adding/subtracting...
x+1<5+1
x+2<5+2
x+a<5+a 
multiples of both sides...
2x<10
2x<15
bx<5b 
In fact many reversible things we do to the left (as well as the right side) are possible :)