how to use ruby " case ... when " with inequalities?

You are mixing two different types of case statements:

case var
when 1
  dosomething
when 2..3
  doSomethingElse
end

case
when var == 1
   doSomething
when var < 12
   doSomethingElse
end

   case myvar
     when  proc { |n| n < -5 }
        do somethingA
     when -5..-3
        do special_something_XX
     when -2..-1
        do special_something_YY
     when proc { |n| n == 0 }
        do somethingB
     when proc { |n| n > 0 }
        go somethingC
     end
   end

I am not personally convinced that you wouldn't be better off with if statements, but if you want a solution in that form:

Inf = 1.0/0

case myvar
when -Inf..-5
  do somethingA
when -5..-3
  do special_something_XX
when -2..-1
  do special_something_YY
when 0
  do somethingB
when 0..Inf
  do somethingC
end

My preferred solution follows. Here the order matters and you have to repeat the myvar, but it's much harder to leave out cases, you don't have to repeat each bound twice, and the strictness (< vs <= rather than .. vs ...) is much more obvious.

if myvar <= -5
  # less than -5
elsif myvar <= -3
  # between -5 and -3
elsif myvar <= -1
  # between -3 and -1
elsif myvar <= 0
  # between -1 and 0
else
  # larger than 0
end

def project_completion(percent)
 case percent
  when  percent..25
    "danger"
  when percent..50
    "warning"
  when percent..75
    "info"
  when percent..100
    "success"
  else
   "info"
  end
end

Using infinity may help

case var
when -Float::INFINITY..-1
when 0
when 1..2
when 3..Float::INFINITY
end