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]}