{x∈R: 14xx+1−9x−30x−4<0}=

Given 14xx+1−9x−30x−4<0⇒ 14x(x−4)−(x+1)(9x−30)(x+1)(x−4)<0⇒ 14x2−56x−9x2+30x−9x+30(x+1)(x−4)<0⇒ 5x2−35x+30(x+1)(x−4)<0⇒ x2−7x+6(x+1)(x−4)<0⇒ (x−1)(x−6)(x+1)(x−4)<0⇒ (x−1)(x−6)(x+1)(x−4)<0∴ x∈ (−1, 1)∪(4, 6)

{x∈R: 14xx+1−9x−30x−4<0}=

Given 14xx+1−9x−30x−4<0⇒ 14x(x−4)−(x+1)(9x−30)(x+1)(x−4)<0⇒ 14x2−56x−9x2+30x−9x+30(x+1)(x−4)<0⇒ 5x2−35x+30(x+1)(x−4)<0⇒ x2−7x+6(x+1)(x−4)<0⇒ (x−1)(x−6)(x+1)(x−4)<0⇒ (x−1)(x−6)(x+1)(x−4)<0∴ x∈ (−1, 1)∪(4, 6)

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

${x \in R : \frac{14 x}{x + 1} - \frac{9 x - 30}{x - 4} < 0} =$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$(- 1, 1) \cup (4, 6)$

$(- 1, 4)$

$(1, 4) \cup (5, 7)$

$(1, 7)$

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} G i v e n \frac{14 x}{x + 1} - \frac{9 x - 30}{x - 4} < 0 \\ \Rightarrow \frac{14 x (x - 4) - (x + 1) (9 x - 30)}{(x + 1) (x - 4)} < 0 \\ \Rightarrow \frac{14 x^{2} - 56 x - 9 x^{2} + 30 x - 9 x + 30}{(x + 1) (x - 4)} < 0 \\ \Rightarrow \frac{5 x^{2} - 35 x + 30}{(x + 1) (x - 4)} < 0 \\ \Rightarrow \frac{x^{2} - 7 x + 6}{(x + 1) (x - 4)} < 0 \\ \Rightarrow \frac{(x - 1) (x - 6)}{(x + 1) (x - 4)} < 0 \\ \Rightarrow (x - 1) (x - 6) (x + 1) (x - 4) < 0 \\ ∴ x \in (- 1, 1) \cup (4, 6) \end{array}$