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📐 Mathematics  ·  Linear Inequalities  ·  JEE

The solution set of |2x − 1| < 3 is:

Answer: (−1, 2).

  • A (−1, 2)
  • B (−2, 1)
  • C (1, 2)
  • D (−1, 1)

Correct answer: A. (−1, 2)

Explanation: −3 < 2x − 1 < 3 gives −2 < 2x < 4, so −1 < x < 2.

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 →