Question

Giải các bất phương trình sau:

a) \(\dfrac{x-2}{1007}+\dfrac{x-1}{1008}< \dfrac{2x-1}{2017}+\dfrac{2x-3}{2015}\)

b) \(\dfrac{3-x}{100}+\dfrac{4-x}{101}>\dfrac{10-2x}{204}+\dfrac{12-2x}{206}\)

Answer 1

a: =>\(\dfrac{2x-4}{2014}+\dfrac{2x-2}{2016}< \dfrac{2x-1}{2017}+\dfrac{2x-3}{2015}\)

=>\(\dfrac{2x-2018}{2014}+\dfrac{2x-2018}{2016}< \dfrac{2x-2018}{2017}+\dfrac{2x-2018}{2015}\)

=>2x-2018<0

=>x<2019

b: \(\Leftrightarrow\left(\dfrac{3-x}{100}+\dfrac{4-x}{101}\right)>\dfrac{5-x}{102}+\dfrac{6-x}{103}\)

=>\(\dfrac{x-3}{100}+\dfrac{x-4}{101}-\dfrac{x-5}{102}-\dfrac{x-6}{103}< 0\)

=>\(x+97< 0\)

=>x<-97