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1. Tell which property or axiom of the real numbers justifies each of the following mathematical statements. a. 2(x+y)= 2x+2y b. x+(2+5)- (x+2) +5 c. 5x(2x3)-(5x2)× 3 d. 2<3=-5x2>-5x3 e. (3y +4)+(2y' +3)=(3y' +2y')+(4+3)=5y' +7

1. Tell which property or axiom of the real numbers justifies each of the following mathematical statements. a. 2(x+y)= 2x+2y b. x+(2+5)- (x+2) +5 c. 5x(2x3)-(5x2)× 3 d. 2<3=-5x2>-5x3 e. (3y +4)+(2y' +3)=(3y' +2y')+(4+3)=5y' +7

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.2: Solving Inequalities
Problem 64WE
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1. Tell which property or axiom of the real numbers justifies each of the following mathematical statements. a. -2x <12 x >-6 b. 2x = 12 2x +3=15 c. 3+x+2= x +2+3=x+5 d. If 11<20 and 20<30, then 11<30. e. If x <0, then x² >0. 2. Write TRUE if the mathematical statement is true, otherwise, write FALSE. a. cx-d =-cxd b. Subtraction is commutative. c. Subtraction is associative. d. Zero (0) is the only real number which is its own additive inverse. e. Adding a negative number to both sides of an inequality reverses the inequality sign.
Transcribed Image Text:1. Tell which property or axiom of the real numbers justifies each of the following mathematical statements. a. -2x <12 x >-6 b. 2x = 12 2x +3=15 c. 3+x+2= x +2+3=x+5 d. If 11<20 and 20<30, then 11<30. e. If x <0, then x² >0. 2. Write TRUE if the mathematical statement is true, otherwise, write FALSE. a. cx-d =-cxd b. Subtraction is commutative. c. Subtraction is associative. d. Zero (0) is the only real number which is its own additive inverse. e. Adding a negative number to both sides of an inequality reverses the inequality sign.
1. Tell which property or axiom of the real numbers justifies each of the following mathematical statements. a. 2(x+y)=2x +2y b. x+(2+5) = (x +2) + 5 c. 5x(2x3)3(5x2)x3 d. 2<3=-5x2>-5x3 e. (3y' +4)+(2y" +3)=(3y² +2y')+(4+3)=5y² +7 2. Give one example that illustrates each of the following axioms. a. Distributivity of multiplication over addition b. Associativity of multiplication c. Transitivity (order) axiom d. Commutativity of addition e. Addition property of equality
Transcribed Image Text:1. Tell which property or axiom of the real numbers justifies each of the following mathematical statements. a. 2(x+y)=2x +2y b. x+(2+5) = (x +2) + 5 c. 5x(2x3)3(5x2)x3 d. 2<3=-5x2>-5x3 e. (3y' +4)+(2y" +3)=(3y² +2y')+(4+3)=5y² +7 2. Give one example that illustrates each of the following axioms. a. Distributivity of multiplication over addition b. Associativity of multiplication c. Transitivity (order) axiom d. Commutativity of addition e. Addition property of equality
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