Question
Download Solution PDFIf \(\frac{4}{x}<\frac{1}{3}\), what is the possible range of values for x?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Rules for Operations on Inequalities:
- Adding the same number to each side of an inequality does not change the direction of the inequality symbol.
- Subtracting the same number from each side of an inequality does not change the direction of the inequality symbol.
- Multiplying each side of an inequality by a positive number does not change the direction of the inequality symbol.
- Multiplying each side of an inequality by a negative number reverses the direction of the inequality symbol.
- Dividing each side of an inequality by a positive number does not change the direction of the inequality symbol.
- Dividing each side of an inequality by a negative number reverses the direction of the inequality symbol.
Calculation:
Given:
\(\frac{4}{x}<\frac{1}{3}\)
\(\Rightarrow \frac{4}{x}-~\frac{1}{3}<0\)
\(\Rightarrow \frac{12-x}{3x}<0\)
\(\Rightarrow \frac{-~\left( x-12 \right)}{3x}<0\)
Multiplying each side of an inequality by a negative number reverses the direction of the inequality symbol.
\(\Rightarrow \frac{\left( x-12 \right)}{3x}>0\), Here x ≠ 0
∴ x < 0 OR x > 12
Last updated on May 15, 2025
->CUET UG hall ticket out for May 19 to May 24, 2025 exams.
-> The CUET 2025 Postponed for 15 Exam Cities Centres.
-> Check out the CUET UG Answer Key 2025 for today's exam.
-> The NTA CUET Admit Card 2025 has been uploaded on May 10, 2025 at the official website.
-> The CUET 2025 Exam Date will be conducted between May 13 to June 3, 2025.
-> The CUET City Intimation Slip 2025 has been uploaded on the official website.
->The CUET UG 2025 Application correction window closed on March 28, 2025.
-> 12th passed students will be appearing for the CUET UG Exam to get admission to UG courses at various colleges and universities.
-> Prepare Using the Latest CUET UG Mock Test Series.
-> Candidates can check the CUET Previous Year Papers, which helps to understand the difficulty level of the exam and experience the same.