Задача 62888 Решить систему неравенств...
Условие
Решение
[m]\left\{\begin {matrix}3x-5 ≤ 7x\\2x+1>-2x+3\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}3x-7x ≤5\\2x+2x>-1+3\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}-4x ≤5\\4x>2\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}x ≥- 1,25\\x>0,5\end {matrix}\right.[/m]
О т в е т. x >0,25 или x ∈ (0,25;+ ∞ )
2)
[m]\left\{\begin {matrix}\frac{x}{3}+\frac{2x-1}{5} < 1\\-\frac{5x+1}{2}-\frac{7}{3}>\frac{x}{5}\end {matrix}\right.[/m]
Умножаем первое уравнение на 15
второе на 30
[m]\left\{\begin {matrix}5x+3(2x-1) <15\\-15(5x+1)-10\cdot 7 > 6x\end {matrix}\right.[/m] ⇒[m]\left\{\begin {matrix}5x+6x-3 <15\\-75x-15- 70 > 6x\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}11x<18\\-81x>85\end {matrix}\right.[/m]
[m]\left\{\begin {matrix}x<\frac{18}{11}\\x<-\frac{85}{81}\end {matrix}\right.[/m]
О т в е т. [m]x<-\frac{85}{81}[/m]
3)
[m]\left\{\begin {matrix}3x+5 ≤ 7x\\2x-1>-3x+3\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}3x-7x ≤-5\\2x+3x>+1+3\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}-4x ≤-5\\5x>4\end {matrix}\right.[/m] ⇒ [m]\left\{\begin {matrix}x ≥ 1,25\\x>0,8\end {matrix}\right.[/m]
О т в е т. x ≥ 1,25 или x ∈ [1,25;+ ∞ )