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📐 Mathematics  ·  Linear Inequalities  ·  JEE

When graphing 2x + 3y <= 12, what kind of boundary line is drawn?

Answer: A solid line.

  • A A dashed line
  • B A solid line
  • C No line is drawn
  • D A curved line

Correct answer: B. A solid line

Explanation: Since the inequality includes equality (<=), the boundary line is solid, meaning points on the line are included.

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 →