Chapter 5: Linear InequalitiesClass 11 Mathematics — summary, notes, extra questions & MCQ quiz

Summary

Many real situations are described not by equations but by inequalities using the symbols \(<,\ >,\ \le,\ \ge\). This chapter studies linear inequalities in one variable. A solution is any value of the variable that makes the inequality true, and the collection of all such values is the solution set, which may be found over \(\mathbb{N}\), \(\mathbb{Z}\) or \(\mathbb{R}\). The rules mirror those for equations: equal numbers may be added to or subtracted from both sides, and both sides may be multiplied or divided by the same positive number — but multiplying or dividing by a negative number reverses the inequality. Solutions over the real numbers are written as intervals such as \((-2,\infty)\) and shown on a number line, with an open circle for a strict inequality and a closed circle for \(\le\) or \(\ge\). Word problems — averages of marks, mixing acid solutions, consecutive odd integers, temperature conversion — are translated into inequalities and solved, illustrating wide use in science, statistics and economics.

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