Решите неравенство даю 10 баллов

$25x^2-3|3-5x|\ \textless \ 30x-9$

раскроем модуль

$3-5x=0 x=3/5=0.6$

$x\ \textless \ 0.6: |3-5x|=3-5x x \geq 0.6: |3-5x|=5x-3$

1) x<0.6<br>
$25x^2-3(3-5x)\ \textless \ 30x-9$

$25x^2-9+15x-30x+9\ \textless \ 0$

$25x^2-15x\ \textless \ 0$

$5x(5x-15)\ \textless \ 0$

___+____0______-_____0.6____+__

x∈(0;0.6)

2) x≥0.6

$25x^2-3(5x-3)\ \textless \ 30x-9$

$25x^2-15x+9-30x+9\ \textless \ 0$

$25x^2-45x+18\ \textless \ 0 D=2025-1800=225=15^2 x_1=1.2; x_2=0.6$

_+___0.6_____-____1.2_____+___

x∈ [0.6; 1.2)

Ответ (0; 1.2)