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📐 Mathematics  ·  Linear Inequalities  ·  JEE

A closed (filled) circle on a number line shows that the endpoint is:

Answer: included.

  • A included
  • B excluded
  • C at infinity
  • D undefined

Correct answer: A. included

Explanation: A filled circle means the endpoint value is part of the solution set (≤ or ≥).

Number Line vs Half-Plane Representationx > 2 (open circle, hollow)2x ≤ 2 (closed circle, filled)shaded regionsatisfies the inequality2D inequality: dashed line = strict, shaded = solution side

One-variable inequalities use open (excluded) or closed (included) circles on a number line; two-variable inequalities use a dashed (strict) or solid (non-strict) boundary line, with the solution being the entire shaded half-plane on one side of it.

Concept context

Solving linear inequalities in one and two variables algebraically and graphically, and representing solutions on a number line or as a region in a plane.

Read the full Linear Inequalities notes →