Question

4.
If x € (-4, 6) then
€
1/x

(a) (-1/4, 1/6)
(b) (-1/4, 1/6]
(c) (-00, -1/4] U (1/6, 00)
(d) (-0, -1/4] [1/6, 0)​

Answer 1

Answer:

(c) $(- \infty, -\frac14) \cup (\frac16, \infty)$

Step-by-step explanation:

$-4 < x < 0^- \text{ OR }0^+<x<6$

Now take the reciprocal of the inequality (note that sign reverses on taking reciprocal)

$-\dfrac14 > \dfrac1x > -\infty \text{ OR }\infty>\dfrac1x>\dfrac16$

$x \in (- \infty, -\frac14) \cup (\frac16, \infty)$