1.
1st major thing done in algebra: write an expresson representing something in the real world
2.
2nd major thing done in algebra: find the value of the expression when you know what x equals
3.
3rd major thing done in algebra: find the value of x when you know what the expression equals
4.
addition property of equality: if a=b, then a+c=b+c; , if you add the same number to each side of an equation, the two sides remain equal
5.
additive identity axiom: a+0=a
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additive inverse axiom: a+(-a)=0
7.
associative axiom of addition: (a+b)+c=a+(b+c)
8.
associative axiom of multiplication: (a•b)•c=a•(b•c)
9.
commutative axiom of addition: a+b=b+a; order does not matter in addition
10.
Commutative axiom of multiplication: ab=ba; order does not matter in multiplication
11.
distributive axiom of multiplication over addition: a(b+c)=ab+ac
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multiplication property of -1: a(-1)=-a
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multiplication property of 0: a0=0
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multiplication property of equality: if a=b, then ac=bc
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multiplicative identity axiom: 1a=a
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multiplicative inverse axiom: ax1/a=1
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reflexive axiom of equality: a=a
18.
symmetric axiom of equality: if a=b then b=a
19.
transitive axiom of equality: if a=b and b=c then a=c