How do you solve #(2t+7)/(t-4)>=3# using a sign chart?

1 Answer
Feb 9, 2017

Answer:

The solution is #t in ]4, 19]#

Explanation:

Rewrite the equation

#(2t+7)/(t-4)>=3#

#(2t+7)/(t-4)-3>=0#

#((2t+7)-3(t-4))/(t-4)>=0#

#(2t+7-3t+12)/(t-4)>=0#

#(-t+19)/(t-4)>=0#

Let #f(t)=(-t+19)/(t-4)#

We can construct the sign chart

#color(white)(aaaa)##t##color(white)(aaaa)##-oo##color(white)(aaaaaaa)##4##color(white)(aaaaaaaa)##19##color(white)(aaaaaa)##+oo#

#color(white)(aaaa)##t-4##color(white)(aaaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aaaaa)##+#

#color(white)(aaaa)##19-t##color(white)(aaaa)##+##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aaaaa)##-#

#color(white)(aaaa)##f(t)##color(white)(aaaaaa)##-##color(white)(aaaa)##||##color(white)(aaaa)##+##color(white)(aaaaa)##-#

Therefore,

#f(t)>=0# when #t in ]4, 19]#