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📐 Mathematics  ·  Linear Inequalities  ·  JEE

The solution set of |x − 2| ≥ 5 is:

Answer: x ≤ −3 or x ≥ 7.

  • A −3 ≤ x ≤ 7
  • B x ≤ −3 or x ≥ 7
  • C x ≥ 7
  • D −7 ≤ x ≤ 3

Correct answer: B. x ≤ −3 or x ≥ 7

Explanation: x − 2 ≤ −5 or x − 2 ≥ 5 gives x ≤ −3 or x ≥ 7.

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 →