Mathematics, 24.10.2020 04:00 hosfordkenya4
DUE TODAY Springboard Practice 7 Question 11 USING THESE PROOFS
Reflexive Property of Equality For all real numbers a, a = a.
Symmetric Property of Equality For all real numbers a and b, if a = b, then b = a.
Transitive Property of Equality For all real numbers a, b, and c, if a = b and b = c, then a = c.
Substitution Property of Equality For all real numbers a and b, if a = b, then a may be replaced by b.
Additive Identity For all real numbers a, a + 0 = 0 + a = a.
Multiplicative Identity For all real numbers a, a β
1 = 1β
a = a.
Commutative Property of
Addition
For all real numbers a and b, a + b = b + a.
Commutative Property of
Multiplication
For all real numbers a and b, a β
b = b β
a.
Associative Property of Addition For all real numbers a, b, and c, (a + b) + c = a + (b + c).
Associative Property of
Multiplication
For all real numbers a, b, and c, (a β
b) β
c = a β
(b β
c).
Distributive Property of
Multiplication over Addition
For all real numbers a, b, and c, a(b + c) = a β
b + a β
c.
Additive Inverse For all real numbers a, there is exactly one real number -a
such that a + (-a) = 0 and (-a) + a = 0.
Multiplicative Inverse For all real numbers a and b where a β 0, b β 0, there is exactly
one number b
a
such that b
a
a
bβ
= 1 and a
b
b
aβ
= 1.
Multiplication Property of Zero For all real numbers a, a β
0 = 0 and 0 β
a = 0.
Addition Property of Equality For all real numbers a, b, and c, if a = b, then a + c = b + c.
Subtraction Property of Equality For all real numbers a, b, and c, if a = b, then a β c = b β c.
Multiplication Property of
Equality
For all real numbers a, b, and c, if a = b, then a β
c = b β
c.
Division Property of Equality For all real numbers a, b, and c, c β 0 if a = b, then a
c
b
c = .
Zero Product Property of Equality For all real numbers a and b, if a β
b = 0 then a = 0 or b = 0 or
both a and b equal 0.
Addition Property of Inequality* For all real numbers a, b, and c, if a > b, then a + c > b + c.
Subtraction Property of
Inequality*
For all real numbers a, b, and c, if a > b, then a β c > b β c.
Multiplication Property of
Inequality *
For all real numbers a, b, and c, c > 0, if a > b, then a β
c > b β
c.
For all real numbers a, b, and c, c b, then a β
c 0 if a > b, then a
c
b
c
> .
For all real numbers a, b, and c, c b, then a
c
b
c
< .
Answers: 3
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DUE TODAY Springboard Practice 7 Question 11 USING THESE PROOFS
Reflexive Property of Equality For...
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