New News Algebra #1

Idea 1: Math = Sentences

5 (subject) = (verb) 2+3 (object) —— Equation: a statement that two things are equal.

9 (subject) > (verb) 5+3 (object) —— Inequality: a statement that describes the relationship between two things that are not equal

Conclusion: both can be represented as sentences using normal punctuation (e.g. commas)

Idea 2: Algebra = Math sentences with variables; Variable = mystery quantity / unknown

When solving algebra equations, we have to answer question: “What does variable have to be to make sentence true?”

Note: variable could be represented by whatever letter (e.g. x, y, z)

Rule: keep both sides of an equation balanced by “+”, “-”, “*”, “/”

∴ e.g1 y=x » y+2=x+2 » 2y=2x » ...

e.g2 a=b » 2a=2b » a/2=b/2 » a+12=b+12

Sub-idea 1: Solution set = all possible outcomes for a variable

e.g.1 (w-55)(w-707)=0 Solution Set {55, 707}

e.g.2 z=z Solution Set {all numbers}

e.g.3 x=x+1 Solution Set {no numbers} « not possible because 0≠1

Note: e.g. 2x-x2=0 » 2x-x2/x=0/x unless (x≠0) because x could equal 0, and dividing by 0 is impossible.