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📐 Mathematics  ·  Linear Inequalities  ·  JEE

Find the solution set of -5 <= 2x - 3 < 7.

Answer: -1 <= x < 5.

  • A -1 <= x < 5
  • B -4 <= x < 2
  • C -1 < x <= 5
  • D 1 <= x < 5

Correct answer: A. -1 <= x < 5

Explanation: Add 3 to all parts: -2 <= 2x < 10. Divide by 2: -1 <= x < 5.

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.

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