Cheat sheet · JEE Preparation Mathematics
Linear Inequalities cheat sheet
The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.
JEE · Mathematics
Cheat sheet
Class 11 · Chapter 5Linear Inequalities
Multiply or divide by a negative number — flip the sign.
1. Rules
- Adding/subtracting the same number keeps the sign.
- Multiplying/dividing by a positive number keeps the sign.
- Multiplying/dividing by a negative number reverses the sign.
2. One Variable
, i.e. .
Show on a number line: filled circle for ≤/≥, hollow for < / >.
3. Two Variables (graphical)
- Draw the line ax + by = c (solid for ≤/≥, dashed for < / >).
- Test a point (often the origin) to pick the half-plane.
- For a system, the solution is the common shaded region.
4. Key Points
- Strict inequality: boundary not included.
- Write answers in interval notation.
- Check the end points.
- Double inequality: work on all three parts.
Remember: Flip on negative | number line | half-planes
Linear Inequalities: questions and notes
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