List manipulation - End loop

Question

Given are two matrices (a & b). I want to end the For-loop if all values in the matrix (a minus b) are smaller than 7, in contrast to any value in the matrix (a minus b) is smaller than 7. Can anybody help me with this problem?

For[Q = 0, Q <= 20, Q += 1,
  Print[Q];
  Print[a = {{40, 40, 40}, {40, 40, 40}, {40, 40, 40}}];
  Print[b = Q {{4, 4, 4}, {4, 3, 4}, {4, 4, 4}}];

   compare[matrix_, length_, width_, value_] := 
   Module[{state}, state = False; For[i = 1, i <= length, i++, 
     For[j = 1, j <= width, j++, 
      If[matrix[[i, j]] < value, state = True]]]; Return[state]];

  If[compare[a - b, 3, 3, 7], Break[],]];

Answer 1

For example:

compare[a_, b_] := And @@ (Less[#, 7] & /@ Flatten@(a - b))

Then

For[Q = 0, Q <= 20, Q += 1, Print[Q];
 Print[a = {{40, 40, 40}, {40, 40, 40}, {40, 40, 40}}];
 Print[b = Q {{4, 4, 4}, {4, 3, 4}, {4, 4, 4}}];
 If[compare[a, b], Break[]]]

Stops at Q=12:

{{40,40,40},{40,40,40},{40,40,40}}

{{48,48,48},{48,36,48},{48,48,48}}

Alternative that may or may not be faster (other members are much, much better at optimizing for speed, if you have this problem you should say so):

compare2[a_, b_] := ! Or @@ Positive@UnitStep@Flatten@(a - b - 7)

Answer 2

If the purpose is to print only the matrices that comply with the constraint (as the last printed are the first exception), perhaps (using the compare function of Anon):

compare[a_, b_] := And @@ (Less[#, 7] & /@ Flatten@(a - b));
a = {{40, 40, 40}, {40, 40, 40}, {40, 40, 40}};
b = {{4, 4, 4}, {4, 3, 4}, {4, 4, 4}};
Q = 0;
While[compare[a, Q b] == False, Print[Q]; Print[a]; Print[Q b]; Q++]