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

1 Answer
Aug 1, 2017

Answer:

#(-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]}