Rules for inequalities

For real numbers X, Y, Z and N

X < Y, if and only if  (Y – X) > 0

If  X < Y and Y < Z , then X < Z

If  X < C then ( X + Z )  <  ( Y + Z )

If  X < Y, then  –  X >  –  Y

If X < Y, then

• N = 0, then X.N = Z.N
• N < 0, then X.N > Y.N
• N > 0, then X.N < Y.N

If  0 < X  < Y, then 0 < 1/X < 1/Y
The basic concept of inequalities is employed in-order to understand the intervals.