Question

How do solve `6/x<2` graphically?

Answer 1

`(-oo,0)uu(3,+oo)`

Explanation:

`"rearrange so that right side is zero"`

`6/x-2<0larrcolor(red)" required solution"`

`"express the left side as a single fraction"`

`rArr(6-2x)/x<0`

`(6-2x)/x" has a vertical asymptote at "x=0`

`"and a horizontal asymptote at "y=-2`

`"solve "6-2x=0rArrx=3larrcolor(red)" x-intercept"`

`"from the graph we are looking for the solutions from"`
`"below the x-axis"`

`"solution is" (-oo,0)uu(3,+oo)`
graph{(6-2x)/x [-10, 10, -5, 5]}