Discussion
If \(x \ne 11\) satisfies the inequality \(\frac{2x - 21}{x - 11} \ge 3\),then x lies in the interval
Answer: B
\(x\) lies in \((11, 12]\).
Move everything to one side over the common denominator:
\[ \frac{2x - 21}{x - 11} - 3 = \frac{12 - x}{x - 11} \ge 0 \]
The fraction is non-negative when numerator and denominator have the same sign (or the numerator is 0): \(12 - x \ge 0\) with \(x - 11 \gt 0\) gives \(11 \lt x \le 12\); the other case is impossible. 12 itself is included (the fraction equals 0); 11 is not. Multiplying through by \(x - 11\) without checking its sign leads to the wrong intervals.
No comment is present. Be the first to comment.
Loading…
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development