How do you solve #x-10/(x-1)>=4# using a sign chart?

1 Answer
Nov 18, 2016

Answer:

The answer is #x in ]-oo,-1 ]uu [6, +oo[#

Explanation:

Let's do some simplification

#x-10/(x-1)>=4#

Multiply by #(x-1)#

#x(x-1)-10>=4(x-1)#

#x^2-x-10>=4x-4#

#x^2-5x-6>=0#

Factorising

#(x+1)(x-6)>=0#

Let #f(x)=(x+1)(x-6)#

let's do a sign chart

#color(white)(aaaa)##x##color(white)(aaaaaa)##-oo##color(white)(aaaa)##-1##color(white)(aaaa)##6##color(white)(aaaa)##+oo#

#color(white)(aaaa)##(x+1)##color(white)(aaaaaa)##-##color(white)(aaa)##+##color(white)(aaa)##+#

#color(white)(aaaa)##(x-6)##color(white)(aaaaaa)##-##color(white)(aaa)##-##color(white)(aaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaaaaa)##+##color(white)(aaa)##-##color(white)(aaa)##+#

#f(x)>=0#, when # x in ]-oo,-1 ]uu [6, +oo[#

graph{(x+1)(x-6) [-17.02, 15.02, -12.81, 3.21]}