Class 11 Maths Chapter 5 Linear Inequalities – Revision Notes

This chapter covers the small but crucial exception to equation-solving rules: multiplying or dividing an inequality by a negative number reverses its direction, and it extends that idea to graphing inequalities on a number line and plane.

Last Updated: September 23, 2026

Rules

• Add/subtract same value: direction unchanged.
• Multiply/divide by positive: direction unchanged.
• Multiply/divide by negative: direction REVERSES.

Number Line

• Open circle: <, > (excluded). Closed circle: ≤, ≥ (included).

Graphing (2 variables)

• Solid line: ≤/≥. Dashed line: </>.
• Test point (often origin) determines which side to shade.

Systems of Inequalities

• Solution = intersection (overlap) of all individual regions.

One-Line Summary

Linear inequalities are solved like equations except multiplying/dividing by a negative reverses the direction, and their solutions are ranges shown on number lines (1 variable) or shaded regions (2 variables), with systems solved by finding the overlapping region.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

How does solving a linear inequality differ from solving a linear equation?
The steps are similar (adding, subtracting, multiplying, dividing both sides), but when multiplying or dividing an inequality by a negative number, the inequality sign must be reversed, which has no equivalent rule for equations.

What does the graphical solution of a linear inequality in two variables represent?
It represents a half-plane region on either side of the boundary line. Every point in that region satisfies the inequality, and the boundary line is included (solid line) or excluded (dashed line) depending on whether the inequality is strict.

Written by Satish

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