How do you solve #1/4<7/(7-x)# using a sign chart?

1 Answer
Jun 6, 2017

Answer:

The solution is #x in (-21,7)#

Explanation:

We cannot do crossing over.

Let's rearrange the equation

#1/4<7/(7-x)#

#7/(7-x)-1/4>0#

#(28-(7-x))/(4(7-x))>0#

#(21+x)/(4(7-x))>0#

Let #f(x)=(21+x)/(4(7-x))#

Let's build the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##-21##color(white)(aaaaaaa)##7##color(white)(aaaaaaa)##+oo#

#color(white)(aaaa)##21+x##color(white)(aaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aaaa)##+#

#color(white)(aaaa)##7-x##color(white)(aaaaaa)##-##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aaaa)##-#

Therefore,

#f(x)>0# when #x in (-21,7)#