If \(\frac{4}{x}<\frac{1}{3}\), what is the possible range of values for x?

  1. x < 3 OR x > 4
  2. x < 0 OR x > 12
  3. x < 3 OR x > 0
  4. x < 0 OR x > 3

Answer (Detailed Solution Below)

Option 2 : x < 0 OR x > 12
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CUET General Awareness (Ancient Indian History - I)
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Detailed Solution

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Concept:

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

F1 A.K 24.4.2 Pallavi D4

∴ x < 0 OR x > 12

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