2.4_Algebra_Properties_and_Proofs

2.4_Algebra_Properties_and_Proofs - 2.4 PROPERTIES AND...

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2.4 PROPERTIES AND PROOFS IN ALGEBRA
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Euclid – the father of geometry •wrote “The Elements” about 300 BC •a book of 13 chapters which we use today for our definitions and postulates and theorems
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PROOFS
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Given: 2x + 3 = 11 Prove: x = 4 2x + 3 = 11 3 = 3 2x = 8 2 = 2 x = 4 1. 5. 3. subtraction prop. 3. 1. given 5. division prop. statements reasons 2. 4. 2. reflexive 4. reflexive
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Use with (=) Addition Property: + If a = b, then a + c = b + c Subtraction Property: - If a = b, then a – c = b – c
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Use with (=) Multiplication Property: x If a = b, then ac = bc Division Property: If a = b and c 0, then ab cc
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Distributive Property: (=)   ac ab c b a
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Simplify: (=) Put like things together on both sides of the = sign.
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Substitution Property: (=) If a = b, then b can replace a in any expression. Ex. If x = y and 5x + 3 = 10 then 5y +3 = 10
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Reflexive Property: Use with = or a a 7 7 AB AB AA ex.   
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Symmetric Property: (= or ) If a b, then b a. If AB CD, then CD AB.
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This note was uploaded on 09/20/2011 for the course ALGEBRA idk taught by Professor White during the Spring '11 term at University of Houston.

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2.4_Algebra_Properties_and_Proofs - 2.4 PROPERTIES AND...

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