Don't let them fool you. This is algebra.
1
a. Replacing equals with equals
b. Adding -12 to both sides
c. Multiplying both sides by 1/9
2
a. Associativity, replacing equals
b. Adding -8 to both sides
c. Multiplying both sides by 1/9
3
a. Distributive law
b. Adding -6x to both sides
c. Multiplying both sides by -1
4.
a. Replace equals with equals
b. Add -6m to both sides
c. Add -5 to both sides
d. Multiply both sides by 1/2
5. Symmetric property
6. Distributive property
7. Reflexive property
8. Transitive property