Question

(2x^2-2x+1)/(2x-1)< =1 25x^2-3|3-5x|< 30x-9

Answer 1

1) $\frac{2x^{2}-2x+1}{2x-1} \leq 1$
$\frac{2x^{2}-2x+1}{2x-1}- \frac{2x-1}{2x-1} \leq 0$
$\frac{2x^{2}-2x+1-2x+1}{2x-1} \leq 0$
$\frac{2*(x^{2}-2x+1)}{2x-1} \leq 0$
$\frac{2*(x-1)^{2}}{2x-1} \leq 0$
1.1) $x-1=0$
$x=1$
1.2) $2x-1\ \textless \ 0$
$x\ \textless \ \frac{1}{2}$

ответ: x∈(-бесконечность; 0.5)U{1} 

2) $25x^2-3*|3-5x|\ \textless \ 30x-9$
2.1) $\left \{ {{3-5x \geq 0} \atop {25x^2-3*(3-5x)\ \textless \ 30x-9}} \right.$
$\left \{ {x \leq 0.6} \atop {25x^2-9+15x-30x+9\ \textless \ 0}} \right.$
$\left \{ {x \leq 0.6} \atop {25x^2-15x\ \textless \ 0}} \right.$
$\left \{ {x \leq 0.6} \atop {x*(5x-3)\ \textless \ 0}} \right.$
$\left \{ {x \leq 0.6} \atop {0\ \textless \ x\ \textless \ 0.6}} \right.$

Решение: 0<x<0.6

2.2) $\left \{ {{3-5x\ \textless \ 0} \atop {25x^2-3*(-3+5x)\ \textless \ 30x-9}} \right.$
$\left \{ {{x\ \textgreater \ 0.6} \atop {25x^2+9-15x-30x+9\ \textless \ 0}} \right.$
$\left \{ {{x\ \textgreater \ 0.6} \atop {25x^2-45x+18\ \textless \ 0}} \right.$
$25x^2-45x+18=0, D=45^{2}-4*25*18=225=15^{2}$
$x_{1}= \frac{45-15}{50}=\frac{30}{50}=0.6$
$x_{2}= \frac{45+15}{50}=\frac{60}{50}=1.2$
$\left \{ {{x\ \textgreater \ 0.6} \atop {0.6\ \textless \ x\ \textless \ 1.2}} \right.$

Решение: 0.6<x<1.2

Общее решение: x∈(0; 0.6)U(0.6; 1.2)