9514 1404 393
Explanation:
There are a few basic rules of Algebra. These are broken apart into numerous special cases and each of those is given a name. Here, you're expected to know the names of those "special case" rules.
The basic ideas are ...
- you can (must) always do the same thing to both sides of the equal sign
- things that are equal can always be substituted for each other
We divide that first idea into several "properties of equality":
- addition property of equality: you can add the same to both sides
- subtraction property of equality: you can subtract the same from both sides
- multiplication property of equality: you can multiply both sides by the same
- division property of equality: you can divide both sides by the same
The second idea is used to give you other properties:
- distributive property: a(b+c) = ab +ac
- transitive property: a = b & b = c ⇒ a = c
- substitution property: a = b & a = c ⇒ b = c
- reflexive property: a = a
- symmetric property: a = b ⇒ b = a
__
3. The rules used in this solution are ...
- given
- distributive property
- subtraction property of equality (subtract 2x)
- addition property of equality (add 15)
- division property of equality (divide by 5)
- symmetric property
__
4. The rules used in this solution are ...
- given
- distributive property
- addition property of equality (add 4x)
- subtraction property of equality (subtract 4)
- division property of equality (divide by 6)
