−aa|x| ≤ a ⟺ −a ≤ x ≤ a⚠ Flip sign when ÷ by negative
Chapter 5 · Class XI Mathematics · NCERT Exercises

Linear Inequalities — Exercises

Solve, Shade, Score — 65 Linear Inequality Problems Completely Solved

📂 2 Exercises 📝 40 Questions 🎓 Easy
▶ Start Exercises 📖 Revise Notes

Exercise Index

①
Exercise 5.1
One-variable inequalities; number line; interval notation
26 Q Easy-Moderate
★
Miscellaneous
Modulus inequalities; word problems; combined systems
14 Q Hard

2 exercise files · 40 total questions

Chapter at a Glance

JEE MainCBSE BoardsBITSAT
7Concepts
5Formulas
EasyDifficulty
3–4%Weightage

Before You Begin

Prerequisites

  • ✓Linear equations in 1 & 2 variables (Class X)
  • ✓Coordinate geometry — lines
  • ✓Number line concepts

Have Ready

  • 🔧Graph paper for Ex 5.2 & 5.3
  • 🔧Ruler
  • 🔧Highlighter for feasible region

Exercise Topic Map

Exercise 5.1Solve linear inequalities in one variable (ax+b<c, ax+b≥c); algebraic manipulation; sign reversal; solution sets; number line representation; interval notation; domain constraints (natural numbers, integers, real numbers); word problems on averages, geometry, and constraints
MiscellaneousModulus inequalities |x−a|<b and |x−a|>b; compound inequalities; real-life word problems; application-based questions; range-based solutions; higher-order reasoning for JEE/competitive exams

Key Formulae

\(\text{Multiply/divide by negative} \Rightarrow \text{flip sign}\)
\(|x| < a \iff -a < x < a\)
\(|x| > a \iff x < -a \text{ or } x > a\)
\(\text{Test }(0,0)\text{ in }ax+by \leq c\text{ to choose side}\)

NCERT Solving Method

Step 1 — Isolate x; flip inequality whenever multiplying/dividing by negative. Step 2 — Express solution as interval; open circle for </>, closed for ≤/≥. Step 3 — Two-variable: draw boundary line (convert to equality); test origin to choose half-plane. Step 4 — Systems: shade all inequalities; feasible region = where ALL shadings overlap.

Continue Your Preparation

📖 Notes Theory & concepts 🧠 MCQs Topic-wise practice 🎯 PYQs JEE · CBSE · BITSAT ⚖️ True–False Topic-wise concept check ➡️ Next Chapter Permutations & Combinations
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