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 Jun 13, 2025
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