Inequality Postulates. If: Reason: The whole is greater than any of its parts. ABC Then: Then:and.
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Transcript of Inequality Postulates. If: Reason: The whole is greater than any of its parts. ABC Then: Then:and.
If:If:
Reason: The whole is greater than any of its parts.Reason: The whole is greater than any of its parts.
A B C
ACBCAB
Then:Then: ABAC andand BCAC
If:If:
Reason: Transitive postulate of inequalities.Reason: Transitive postulate of inequalities.
Then:Then: CDAB
BCAB andand CDBC
If A>B and C=BIf A>B and C=B
Reason: Substitution postulate of inequalities.Reason: Substitution postulate of inequalities.
Then: A>CThen: A>C
Addition Postulate 1Addition Postulate 1
If A<B and C=D, then A+C<B+DIf A<B and C=D, then A+C<B+D
Reason: When equal quantities are added to unequal Reason: When equal quantities are added to unequal quantities, their sums are unequal in the same order.quantities, their sums are unequal in the same order.
Addition Postulate 2Addition Postulate 2
If A<B and C<D, then A+C<B+DIf A<B and C<D, then A+C<B+D
Reason: When unequal quantities are added to unequal Reason: When unequal quantities are added to unequal quantities, their sums are unequal in the same order.quantities, their sums are unequal in the same order.
Subtraction PostulateSubtraction Postulateof Inequalitiesof Inequalities
If A<B and C=D, then A-C<B-DIf A<B and C=D, then A-C<B-D
Reason: When equal quantities are subtracted from unequal Reason: When equal quantities are subtracted from unequal quantities, their differences are unequal in the same order.quantities, their differences are unequal in the same order.
Reason: Subtraction postulate of inequalitiesReason: Subtraction postulate of inequalities
Multiplication Postulate of =Multiplication Postulate of =
If A<B and C is a positive number, then AC<BCIf A<B and C is a positive number, then AC<BC
Reason: When unequal quantities are multiplied by equal Reason: When unequal quantities are multiplied by equal quantities, their products are unequal in the same order.quantities, their products are unequal in the same order.
Reason: Multiplication postulate of inequalities.Reason: Multiplication postulate of inequalities.
Division Postulate of =Division Postulate of =
If A<B and C is a positive number, thenIf A<B and C is a positive number, then
Reason: When unequal quantities are divided by equal Reason: When unequal quantities are divided by equal quantities, their quotients are unequal in the same order.quantities, their quotients are unequal in the same order.
Reason: Division postulate of inequalities.Reason: Division postulate of inequalities.
C
B
C
A