Topics Covered
7 key topics in this chapter
Study Resources
Key Formulae
Essential mathematical expressions for this chapter — understand derivations, not just results.
Exam-Ready Insights
Important points to remember — curated from CBSE Board question patterns.
CBSE awards 4 marks for graphical solution of a system of linear inequalities — always shade the feasible region clearly.
When dividing an inequality by a variable, check its sign — if unknown, split into cases.
Number line representation is mandatory in CBSE board answers for 1-variable inequalities.
The word "between" in a problem implies a compound inequality: a < x < b.
Closed circle (●) on number line means the endpoint is included (≤); open circle (○) means excluded (<).
Competitive Exam Strategy
Targeted tips for JEE Main, JEE Advanced, NEET, BITSAT, and KVPY.
Inequalities in JEE are usually linked with quadratics — factor the quadratic, mark sign changes on the number line (wavy curve method).
Absolute value inequalities |f(x)| < g(x): always check that g(x) > 0 first.
BITSAT tests solution sets of systems rapidly — sketch a quick number line or xy-plane region rather than algebraically solving each time.
Integer solutions in a given range: list boundary values and check which integers satisfy the inequality — KVPY counts these frequently.
Common Mistakes to Avoid
Forgetting to flip the inequality when multiplying by a negative number.
Using "=" instead of "∈" when writing solution in interval notation.
Not shading the correct half-plane in 2-variable problems — always test a point (e.g., origin).
Confusing strict inequality (<) with non-strict (≤): impacts whether endpoints are included.
Key Takeaways
The solution set of an inequality is a range of values, not a single point.
Adding/subtracting the same quantity to both sides does NOT change the inequality direction.
Multiplying or dividing by a NEGATIVE number REVERSES the inequality sign.
In 2 variables, the feasible region is a half-plane; a system gives an intersection of half-planes.
Linear programming problems (LP) in Class XII build directly on this chapter.