Real Numbers-Write in Interval Form

Question

$|5 - x^{-1}| \lt 1$

$-1 \lt 5 -\frac{1}{x} \lt 1$.

$-1-5 \lt -\frac{1}{x} \lt 1-5$.

$-6 < -\frac{1}{x}< -4$.

$6 > \frac{1}{x} > 4$.

$6x > 1 > 4x$.

I get stuck after this

Answer 1

$-1 \lt 5 - \frac{1}{x} \lt 1$

$-6 \lt -\frac{1}{x} \lt -4$

$4 \lt \frac{1}{x} \lt 6$

$\frac{1}{6}\lt x \lt \frac{1}{4}$

$(\frac{1}{6},\frac{1}{4})$