Question

How do you solve `\frac { - 9} { 5x + 4} < 0`?

Answer 1

`x in(-4/5,oo)`

Explanation:

`"Calculate the zero of the denominator"`

`5x+4=0rArrx=-4/5`

`"This value splits the domain into 2 intervals"`

`(-oo,-4/5)" and "(-4/5,oo)`

`"select a "color(red)"test point in each interval"`

`x=-1to-9/(-5+4)=9>0`

`x=1to-9/(5+4)=-1<0larrcolor(blue)"satisfies inequality"`

`x in(-4/5,oo)" is the required solution"`
graph{-9/(5x+4) [-10, 10, -5, 5]}