Rule - 1:  Equal numbers may be added to (or subtracted from) both sides of an equation.

      Rule - 2:  Both sides of an equation may be multiplied (or divided) by the same non-zero number. 
    

      Rule - 1:   Equal numbers may be added to (or subtracted from) both sides of an inequality without affecting the sign of inequality.

      Rule - 2:   Both sides of an inequality can be multiplied (or divided) by the same positive number. But when both sides are multiplied or divided by a negative number, then the sign of inequality is reversed.