Question

Giải bất phương trính sau:

\(\dfrac{2x-16}{17}+\dfrac{2x-20}{15}+3\le\dfrac{2x-11}{13}+\dfrac{2x-6}{11}\)

Answer 1

Lời giải:
BPT $\Leftrightarrow \frac{2x-16}{17}-2+\frac{2x-20}{15}-2\leq \frac{2x-11}{13}-3+\frac{2x-6}{11}-4$

$\Leftrightarrow \frac{2x-50}{17}+\frac{2x-50}{15}\leq \frac{2x-50}{13}+\frac{2x-50}{11}$

$\Leftrightarrow (2x-50)\left(\frac{1}{17}+\frac{1}{15}-\frac{1}{13}-\frac{1}{11}\right)\leq 0$

$\Leftrightarrow 2x-50\geq 0$

$\Leftrightarrow x\geq 25$

Vậy BPT có nghiệm $x\mathbb{R}|x\geq 25$