Linear Inequalities · Class 11 · CBSE · Science Mathematics
For a real parameter k, solve the inequality (k - 2)x ≤ 3, giving the solution set separately for k > 2, k = 2, and k < 2.
Practice question from Linear Inequalities (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.
hard · Subjective · Q-17C4BA
For a real parameter k, solve the inequality (k - 2)x ≤ 3, giving the solution set separately for k > 2, k = 2, and k < 2.
Answer: If k > 2, then x ≤ 3/(k - 2). If k = 2, the inequality becomes 0 ≤ 3, which is true for every real x. If k < 2, division by the negative number k - 2 reverses the inequality, so x ≥ 3/(k - 2).
Solution
The sign of the coefficient of determines whether the inequality sign is preserved or reversed. For , the variable term vanishes and the resulting statement is always true.
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