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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

6.
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

12.
multiplication property of 0: a0=0

13.
multiplication property of -1: a(-1)=-a

14.
multiplication property of equality: if a=b, then ac=bc

15.
multiplicative identity axiom: 1a=a

16.
multiplicative inverse axiom: ax1/a=1

17.
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

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