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📐 Mathematics  ·  Linear Inequalities  ·  JEE

If the origin (0,0) satisfies the inequality 4x + 3y <= 12, which side is shaded?

Answer: The side containing the origin.

  • A The side away from the origin
  • B The side containing the origin
  • C Both sides equally
  • D Neither side

Correct answer: B. The side containing the origin

Explanation: Since the test point (0,0) satisfies the inequality (0 <= 12), the half-plane containing the origin is shaded.

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 →