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📐 Mathematics  ·  Linear Inequalities  ·  JEE

If x is a natural number satisfying 5x - 3 < 3x + 7, how many positive integer solutions are there?

Answer: 4.

  • A 4
  • B 5
  • C Infinitely many
  • D 0

Correct answer: A. 4

Explanation: Solve: 5x-3<3x+7 ⟹ 5x-3x<7+3 ⟹ 2x<10 ⟹ x<5. Natural numbers less than 5: {1, 2, 3, 4}. Count = 4. (x=0 excluded as 0 is not a natural number in NCERT convention.) Answer: 4 positive integer solutions

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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