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📐 Mathematics  ·  Linear Inequalities  ·  JEE

The solution region of a linear inequality in two variables is called a:

Answer: Half-plane.

  • A Line segment
  • B Half-plane
  • C Single point
  • D Circle

Correct answer: B. Half-plane

Explanation: A linear inequality in two variables divides the plane into two half-planes; the solution set is one of these half-planes.

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 →