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1.
x ∈ (0; 3/5]
2.
![left { {{3-5x textless 0} atop {25x^2+3(3-5x) textless 30x-9}} right. \ \ left { {{3-5x textless 0} atop {25x^2+9-15x textless 30x-9}} right. \ \ left { {{3-5x textless 0} atop {25x^2-45x+18 textless 0}} right. \ \ 25x^2-45x+18=0 \
D = 2025-1800=225 \
x_1= frac{45-15}{50} = frac{3}{5} \ x_2= frac{45+15}{50} = frac{6}{5} \ left { {{3-5x textless 0} atop {25(x- frac{3}{5} )(x- frac{6}{5}) textless 0}} right.](https://tex.z-dn.net/?f=left+%7B+%7B%7B3-5x++textless+++0%7D+atop+%7B25x%5E2%2B3%283-5x%29+textless++30x-9%7D%7D+right.+%5C+%5C+left+%7B+%7B%7B3-5x++textless+++0%7D+atop+%7B25x%5E2%2B9-15x+textless++30x-9%7D%7D+right.+%5C+%5C+left+%7B+%7B%7B3-5x++textless+++0%7D+atop+%7B25x%5E2-45x%2B18+textless++0%7D%7D+right.+%5C+%5C+25x%5E2-45x%2B18%3D0+%5C+%0AD+%3D+2025-1800%3D225+%5C+%0Ax_1%3D+frac%7B45-15%7D%7B50%7D+%3D+frac%7B3%7D%7B5%7D++%5C+x_2%3D+frac%7B45%2B15%7D%7B50%7D+%3D+frac%7B6%7D%7B5%7D++%5C+left+%7B+%7B%7B3-5x++textless+++0%7D+atop+%7B25%28x-+frac%7B3%7D%7B5%7D+%29%28x-+frac%7B6%7D%7B5%7D%29+textless++0%7D%7D+right. "left { {{3-5x textless 0} atop {25x^2+3(3-5x) textless 30x-9}} right. \ \ left { {{3-5x textless 0} atop {25x^2+9-15x textless 30x-9}} right. \ \ left { {{3-5x textless 0} atop {25x^2-45x+18 textless 0}} right. \ \ 25x^2-45x+18=0 \
D = 2025-1800=225 \
x_1= frac{45-15}{50} = frac{3}{5} \ x_2= frac{45+15}{50} = frac{6}{5} \ left { {{3-5x textless 0} atop {25(x- frac{3}{5} )(x- frac{6}{5}) textless 0}} right.")
![left { {{5x-3 textgreater 0} atop {5(5x- 3)(x- frac{6}{5}) textless 0}} right. \ \left { {{5x-3 textgreater 0} atop {x- frac{6}{5} textless 0}} right. \ \left { {{x textgreater frac{3}{5} } atop {x textless frac{6}{5}}} right. \ \](https://tex.z-dn.net/?f=left+%7B+%7B%7B5x-3+textgreater+++0%7D+atop+%7B5%285x-+3%29%28x-+frac%7B6%7D%7B5%7D%29+textless++0%7D%7D+right.+%5C+%5Cleft+%7B+%7B%7B5x-3+textgreater+++0%7D+atop+%7Bx-+frac%7B6%7D%7B5%7D+textless++0%7D%7D+right.+%5C+%5Cleft+%7B+%7B%7Bx+textgreater+++frac%7B3%7D%7B5%7D+%7D+atop+%7Bx+textless+++frac%7B6%7D%7B5%7D%7D%7D+right.+%5C+%5C "left { {{5x-3 textgreater 0} atop {5(5x- 3)(x- frac{6}{5}) textless 0}} right. \ \left { {{5x-3 textgreater 0} atop {x- frac{6}{5} textless 0}} right. \ \left { {{x textgreater frac{3}{5} } atop {x textless frac{6}{5}}} right. \ \")
x ∈ (3/5; 6/5)
Объединяя два решения, окончательно получаем: x ∈ (0; 6/5).
x ∈ (0; 3/5]
2.
x ∈ (3/5; 6/5)
Объединяя два решения, окончательно получаем: x ∈ (0; 6/5).
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