let's bear in mind that another way to write ⌈x + 3⌉, is by ceil( x + 3 ), since that'd be the "ceil" function, meaning, any decimal gets "ceiled" or hits the integer ceiling.
For example for say x = -1.6, then x + 3 becomes -1.6 + 3 = 1.4, now what's the ceiling for 1.4? or namely, what's the highest integer that's between? well, is between the integers of 1 and 2, the "ceiling" will be 2, so the 1.4 becomes 2, same is true for 1.1 or 1.0000001 or 1.999999, they all "hit the ceiling".
Check the picture below.