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📐 Mathematics  ·  Linear Inequalities  ·  JEE

A student scored 62 and 48 in two tests. What minimum score in a third test (out of 100) gives an average of at least 60?

Answer: 70.

  • A 70
  • B 65
  • C 60
  • D 75

Correct answer: A. 70

Explanation: Let third score be x. (62+48+x)/3 >= 60, so 110+x >= 180, x >= 70.

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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