How do you solve #(x-1)(3x-4)>=0# using a sign chart?

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Answer 1 · 2016-12-06T08:32:52

The answer is #x in ] -oo,1 ] uu [ 4/3, +oo[ #

Let #f(x)=(x-1)(3x-4)#

Let's do the sign chart

#color(white)(aaaa)##x##color(white)(aaaa)##-oo##color(white)(aaaa)##1##color(white)(aaaa)##4/3##color(white)(aaaa)##+oo#

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

#color(white)(aaaa)##3x-4##color(white)(aaaa)##-##color(white)(aaa)##-##color(white)(aaaa)##+#

#color(white)(aaaa)##f(x)##color(white)(aaaaaa)##+##color(white)(aaaa)##-##color(white)(aaaa)##+#

So, #f(x)>=0# for #x in ] -oo,1 ] uu [ 4/3, +oo[ #

graph{y=(x-1)(3x-4) [-1.863, 3.006, -1.232, 1.2]}