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📐 Mathematics  ·  Linear Inequalities  ·  JEE

To decide which side of a boundary line to shade, what is commonly used?

Answer: A test point such as the origin.

  • A A protractor to measure the boundary angle
  • B A test point such as the origin
  • C The slope of the line, considered by itself
  • D Trial and error without any systematic method

Correct answer: B. A test point such as the origin

Explanation: A convenient test point (often the origin, if not on the line) is substituted into the inequality to see which half-plane satisfies it.

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 →