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📐 Mathematics  ·  Linear Inequalities  ·  JEE

Solve: |2x - 3| < 5 is equivalent to which compound inequality (ignoring absolute value notation)?

Answer: -5 < 2x - 3 < 5.

  • A -5 < 2x - 3 < 5
  • B 2x - 3 < 5 alone, ignoring the lower bound
  • C 2x - 3 > -5 alone, ignoring the upper bound
  • D 2x - 3 = 5, treating it as an equation rather than inequality

Correct answer: A. -5 < 2x - 3 < 5

Explanation: An inequality of the form |A| < k (k > 0) is equivalent to -k < A < k, here giving -5 < 2x-3 < 5, i.e. -1 < x < 4.

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 →