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📐 Mathematics  ·  Linear Inequalities  ·  JEE

If x > 5, what happens to the inequality if both sides are multiplied by -1?

Answer: It reverses: -x < -5.

  • A It stays the same: -x > -5
  • B It reverses: -x < -5
  • C It becomes an equation
  • D It becomes undefined

Correct answer: B. It reverses: -x < -5

Explanation: Multiplying or dividing both sides of an inequality by a negative number reverses the inequality sign.

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 →