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📐 Mathematics  ·  Linear Inequalities  ·  JEE

Solve the inequality (2x-1)/(x+3) <= 1, for x not equal to -3.

Answer: -3 < x <= 4.

  • A x < -3 or x > 4
  • B -3 < x <= 4
  • C -3 <= x < 4
  • D x <= -3 or x >= 4

Correct answer: B. -3 < x <= 4

Explanation: Rearranging gives (x-4)/(x+3) <= 0. Testing sign intervals around the critical points x=-3 (excluded) and x=4 shows the expression is negative or zero exactly when -3 < 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 →