Сложно неравенство за 7 клас

[Гост]

20240421_194113.jpg (8.56 KiB) Прегледано 154 пъти

[ammornil]

[tex]\left(\underbrace{\frac{x}{4}-5}_{4}\right)\left(\underbrace{\frac{x}{5}+4}_{5}\right)-\frac{x+5}{2}\cdot{}\left(\underbrace{\frac{3x}{5}-\frac{x+1}{2}}_{10}\right)\le{}x-20 \\ \phantom{q} \\ \frac{x-20}{4}\cdot{}\frac{x+20}{5}-\frac{x+5}{2}\cdot{}\frac{2\cdot{}3x-5\cdot(x+1)}{10}\le{}x-20 \\ \phantom{q} \\ \frac{x^{2}-20^{2}}{20}-\frac{x+5}{2}\cdot{}\frac{6x-5x-5}{10}\le{}x-20 \\ \phantom{q} \\ \frac{x^{2}-20^{2}}{20}-\frac{(x+5)(x-5)}{20}\le{}x-20 \\ \phantom{q} \\ \frac{x^{2}-20^{2}-(x^{2}-5^{2})}{20}-x+20\le{}0 \\ \phantom{q} \\ \frac{x^{2}-400-x^{2}+25}{20}-x+20\le{}0 \\ \phantom{q} \\ -x+20-\frac{375}{20}\le{}0 \\ \phantom{q} \\ x-20+\frac{75}{4}\ge{0} \\ \phantom{q} \\ x \ge{} 20-\frac{75}{4} \\ \phantom{q} \\ x\ge{}\frac{5}{4}[/tex]