Which of following is not reducible to a linear inequation ?

1. $3 - \dfrac{7}{x} \lt 5$

2. $8 + \dfrac{3}{x} \ge \dfrac{5}{x} - 4$

3. $\dfrac{6}{x} - 8 \gt \dfrac{4}{x} + 3x$

4. $\dfrac{3}{x - 1} - 7 \lt 9$

Solving option 3,

$\Rightarrow \dfrac{6}{x} - 8 \gt \dfrac{4}{x} + 3x\\[1em] \Rightarrow \dfrac{6 - 8x}{x} \gt \dfrac{4 + 3x^2}{x} \\[1em]$

Case 1 : If x is positive,

$\Rightarrow 6 - 8x \gt 4 + 3x^2 \\[1em] \Rightarrow 4 + 3x^2 \lt 6 - 8x \\[1em] \Rightarrow 3x^2 + 8x \lt 6 - 4 \\[1em] \Rightarrow 3x^2 + 8x \lt 2 \\[1em]$

Case 2 : If x is negative,

$\Rightarrow 6 - 8x \lt 4 + 3x^2 \\[1em] \Rightarrow 4 + 3x^2 \gt 6 - 8x \\[1em] \Rightarrow 3x^2 + 8x \gt 6 - 4 \\[1em] \Rightarrow 3x^2 + 8x \gt 2 \\[1em]$

Since, the highest power of x is 2 in both the cases,

$\dfrac{6}{x} - 8 \gt \dfrac{4}{x} + 3x$ is not reducible to linear inequation.

Hence, Option 3 is the correct option.