Answer:
Hence final answer is [tex]x<-8[/tex] or [tex]x>\frac{1}{5}[/tex]
correct choice is B because both ends are open circles.
Step-by-step explanation:
Given inequality is [tex]\frac{x+8}{5x-1}>0[/tex]
Setting both numerator and denominator =0 gives:
x+8=0, 5x-1=0
or x=-8, 5x=1
or x=-8, x=1/5
Using these critical points, we can divide number line into three sets:
[tex](-\infty,-8)[/tex], [tex]\left(-8,\frac{1}{5}\right)[/tex] and [tex](\frac{1}{5},\infty)[/tex]
We pick one number from each interval and plug into original inequality to see if that number satisfies the inequality or not.
Test for [tex](-\infty,-8)[/tex].
Clearly x=-9 belongs to [tex](-\infty,-8)[/tex] interval then plug x=-9 into [tex]\frac{x+8}{5x-1}>0[/tex]
[tex]\frac{-9+8}{5(-9)-1}>0[/tex]
[tex]\frac{-1}{-46}>0[/tex]
[tex]\frac{1}{46}>0[/tex]
Which is TRUE.
Hence [tex](-\infty,-8)[/tex] belongs to the answer.
Similarly testing other intervals, we get that only [tex](-\infty,-8)[/tex] and [tex](\frac{1}{5},\infty)[/tex] satisfies the original inequality.
Hence final answer is [tex]x<-8[/tex] or [tex]x>\frac{1}{5}[/tex]
correct choice is B because both ends are open circles.
