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📐 Mathematics  ·  Linear Inequalities  ·  JEE

Solve: 2(x - 3) <= 3x - 2

Answer: x >= -4.

  • A x >= -4
  • B x <= -4
  • C x >= 4
  • D x <= 4

Correct answer: A. x >= -4

Explanation: 2x - 6 <= 3x - 2, so -6 + 2 <= 3x - 2x, giving -4 <= x, i.e. 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 →