Question

Giải các bất phương trình sau:

a) \(\frac{x+2}{98}+\frac{x+3}{97}>\:\frac{x+4}{96}+\frac{x+5}{95}\)

b) \(\frac{x-10}{5}+\frac{x-9}{6}< \frac{x-8}{7}+\frac{x-7}{8}\)

GIÚP MK VỚI, HU HU~~~~~

Answer 1

a) BPT <=> \(\left(\frac{x+2}{98}+1\right)+\left(\frac{x+3}{97}+1\right)>\left(\frac{x+4}{96}+1\right)+\left(\frac{x+5}{95}+1\right)\)

<=> \(\frac{x+100}{98}+\frac{x+100}{97}>\frac{x+100}{96}+\frac{x+100}{95}\)

<=> \(\left(x+100\right)\left(\frac{1}{98}+\frac{1}{97}-\frac{1}{96}-\frac{1}{95}\right)>0\)

Mà \(\frac{1}{98}+\frac{1}{97}-\frac{1}{96}-\frac{1}{95}< 0\)

<=> x + 100 < 0

<=> x < -100

b) BPT <=> \(\left(\frac{x-10}{5}-1\right)+\left(\frac{x-9}{6}-1\right)< \left(\frac{x-8}{7}-1\right)+\left(\frac{x-7}{8}-1\right)\)

<=> \(\frac{x-15}{5}+\frac{x-15}{6}< \frac{x-15}{7}+\frac{x-15}{8}\)

<=> \(\left(x-15\right)\left(\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}\right)< 0\)

Mà \(\frac{1}{5}+\frac{1}{6}-\frac{1}{7}-\frac{1}{8}>0\)

<=> x - 15 < 0

<=> x < 15