Zaymiey

📐 Mathematics  ·  Linear Inequalities  ·  JEE

The solution set of 1/(x − 1) < 2 (x ≠ 1) is:

Answer: x 3/2.

  • A x < 1 or x > 3/2
  • B 1 < x < 3/2
  • C x > 3/2
  • D x < 1

Correct answer: A. x < 1 or x > 3/2

Explanation: For x > 1 the inequality gives x > 3/2; for x < 1 the left side is negative and always less than 2. Solution: x < 1 or x > 3/2.

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 →