The correct option is 6x 5/4x+1 lt;0 Case 1:6x 5 gt;0 and 4x+1 lt;0 ⇒ x gt;5/6 and x lt; 1/4 This is not possible. Case 2:6x 5 lt;0 and 4x+1 ...

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Properties of Inequalities

6 x-5/44+1<0

Question

$\frac{6 x - 5}{4 x + 1} < 0$

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Solution

$\frac{6 x - 5}{4 x + 1} < 0 C a s e 1 : 6 x - 5 > 0 a n d 4 x + 1 < 0 \Rightarrow x > \frac{5}{6} a n d x < \frac{- 1}{4} T h i s i s n o t p o s s i b l e . C a s e 2 : 6 x - 5 < 0 a n d 4 x + 1 > 0 \Rightarrow x < \frac{5}{6} a n d x > \frac{- 1}{4} ∴ S o l u t i o n s e t i s (\frac{- 1}{4}, \frac{5}{6})$

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