FLIP
Multiply by Negative
Multiplying or dividing both sides by a negative number flips the inequality sign.
a < b, k<0 → ka > kb
KEEP
Multiply by Positive
Multiplying or dividing by a positive number keeps the sign the same.
a < b, k>0 → ka < kb
ADD-OK
Addition Property
Adding or subtracting the same value from both sides never changes the direction.
a < b → a+c < b+c
CHAIN
Transitivity
If a < b and b < c, then a < c. Chain inequalities step by step.
a<b, b<c → a<c
PROOF
Proof Structure
Start from what's given → apply properties → reach the goal. Never skip steps.
Given → Steps → QED
ISO
Isolate the Variable
Solving an inequality = isolate x. Watch for sign flip when dividing by negatives!
-2x > 4 → x < -2