Question

Tìm tất cả các nghiệm nguyên âm của bất pt sau: \(\dfrac{2x-1}{4}-\dfrac{x+7}{5}\)≤\(\dfrac{2x+5}{2}\)

Answer 1

\(\dfrac{2x-1}{4}-\dfrac{x+7}{5}\le\dfrac{2x+5}{2}\)

\(\Leftrightarrow\dfrac{2x-1}{4}-\dfrac{x+7}{5}-\dfrac{2x+5}{2}\le0\)

\(\Leftrightarrow\dfrac{5\left(2x-1\right)-4\left(x+7\right)-10\left(2x+5\right)}{20}\le0\)

\(\Leftrightarrow10x-5-4x-28-20x-50\le0\)

\(\Leftrightarrow-34x\le83\)

\(\Leftrightarrow x\ge-\dfrac{83}{34}\)

Vậy pt có nghiệm là \(S=\left\{x|-\dfrac{83}{34}\le x< 0\right\}\)