Inequalities are not equations to solve. Each symbol is a one-way relation - build the safest chain and check whether a conclusion is truly forced.
Every inequality question is the same move: decode the symbols, lay out one clean chain, and test each conclusion against it.
Read >, <, =, ≥, ≤ without ever reversing meaning.
= allows replacement; ≥ is weaker than >.
A > B > C gives A > C. A > B < C does not.
A conclusion follows only if forced in every case.
Complementary pairs can be valid together.
Decode #, @, $, % into standard signs first.
Spot when two terms have no valid bridge.
Decide if statements build a definite comparison.
Mini test + cheat sheet to lock it in.
Master the direction of a symbol and the weight of an equality, and the rest is just chaining.
A > B means A is greater than B. Read it the same way every time; never flip it mid-solve.
Set each link, then watch the verdict for A vs D. Same-direction links carry through; mix a greater with a smaller and the bridge breaks.
Build the comparison structure once, then judge each conclusion independently against it.
Convert any coded signs into standard >, <, =, ≥, ≤ before thinking about conclusions.
Rewrite statements as one clean left-to-right chain. Mark equalities and weak signs separately.
For each conclusion, search for a continuous valid path between the two terms.
On a mixed chain, carry the weakest safe relation. Accept only what is definitely true.
Recognize the format fast and you already know whether to decode, chain, or hunt for a broken bridge.
Watch a clean chain and a broken chain resolve conclusion by conclusion.
Tap any card to flip from the wrong instinct to the correction.
Small disciplines that keep the direction honest under time pressure.
Convert coded signs to standard symbols before touching the conclusions.
For longer chains, sketch left-to-right arrows so direction stays visible.
Test each conclusion independently - do not carry bias from the first.
Keep ≥ and ≤ in mind right up to the final verdict.
When nothing connects two terms, mark no definite relation immediately.
In timed tests, use option elimination only once the chain is clear.
Mixed difficulty, no timer. Every answer comes with a worked explanation and a diagram.
The chain rules that decide every conclusion.
| Chain | Definite conclusion |
|---|---|
| A > B > C | A > C |
| A ≥ B > C | A > C |
| A > B ≥ C | A > C |
| A ≥ B ≥ C | A ≥ C (not A > C) |
| A > B < C | no relation |
| = | two-way replacement |
| ≥ / ≤ | weaker than > / < |
| either-or | only if complementary & exhaustive |
Practice the hard stuff, queue the next topic, or revisit what tripped you up.
