Question #bfc27

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Answer 1 · 2017-04-15T15:04:36

The solution is #x in (1, 10/3)#

We cannot do crossing over

So, let's rearrange the inequality

#(2x+5)/(x-1)>5#

#(2x+5)/(x-1)-5>0#

#((2x+5)-5(x-1))/(x-1)>0#

#(2x+5-5x+5)/(x-1)>0#

#(10-3x)/(x-1)>0#

Let #f(x)=(10-3x)/(x-1)#

We can build a sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##1##color(white)(aaaaaaa)##10/3##color(white)(aaaa)##+oo#

#color(white)(aaaa)##x-1##color(white)(aaaa)##-##color(white)(aa)##||##color(white)(aaaa)##+##color(white)(aaaa)##+#

#color(white)(aaaa)##10-3x##color(white)(aa)##+##color(white)(aa)##||##color(white)(aaaa)##+##color(white)(aaaa)##-#

#color(white)(aaaa)##f(x)##color(white)(aaaaa)##-##color(white)(aa)##||##color(white)(aaaa)##+##color(white)(aaaa)##-#

Therefore,

#f(x)>0# when #x in (1, 10/3)#