Решите дча примера на листочке
Кстати, эти неравенства уже когда-то давно были решены https://znanija.com/task/892875 и https://znanija.com/task/892839
Решить неравенства:
5. |x²-8x+15|≤|15-x²|
6. 3|x-2|+|5x-4|≤10
Решение:
___+___[0]___-___[15/4]___+___[4]___-___
![\boxed 6 \\ \\ \tt 3|x-2|_{(1)}+|5x-4|_{(2)} \leq 10 \\ \\ x-2=0 \ \ \Rightarrow \ \ x=2 \\ 5x-4=0 \ \ \Rightarrow \ \ x=0,8 \\ \\ 1) \ \ x<0,8 \ \ (1-, \ 2-) \\ \\ -3x+6-5x+4 \leq 10 \\ -8x \leq 0 \\ x \geq 0 \\ \\ x \in [0; \ 0,8) \\ \\ 2) \ \ x \in [0,8; \ 2) \ \ (1-, \ 2+) \\ \\ -3x+6+5x-4 \leq 10 \\ 2x \leq8 \\ x \leq 4 \\ \\x \in [0,8; \ 2) \\ \\ 3) \ \ x \geq 2 \ \ (1+, \ 2+) \\ \\ 3x-6+5x-4 \leq 10 \\ 8x \leq 20 \\ x \leq 2,5 \\ \\ x \in [2; \ 2,5]](https://tex.z-dn.net/?f=+%5Cboxed+6+%5C%5C+%5C%5C+%5Ctt+3%7Cx-2%7C_%7B%281%29%7D%2B%7C5x-4%7C_%7B%282%29%7D+%5Cleq+10+%5C%5C+%5C%5C+x-2%3D0+%5C+%5C+%5CRightarrow+%5C+%5C+x%3D2+%5C%5C+5x-4%3D0+%5C+%5C+%5CRightarrow+%5C+%5C+x%3D0%2C8+%5C%5C+%5C%5C+1%29+%5C+%5C+x%3C0%2C8+%5C+%5C+%281-%2C+%5C+2-%29+%5C%5C+%5C%5C+-3x%2B6-5x%2B4+%5Cleq+10+%5C%5C+-8x+%5Cleq+0+%5C%5C+x+%5Cgeq+0+%5C%5C+%5C%5C+x+%5Cin+%5B0%3B+%5C+0%2C8%29+%5C%5C+%5C%5C+2%29+%5C+%5C+x+%5Cin+%5B0%2C8%3B+%5C+2%29+%5C+%5C+%281-%2C+%5C+2%2B%29+%5C%5C+%5C%5C+-3x%2B6%2B5x-4+%5Cleq+10+%5C%5C+2x+%5Cleq8+%5C%5C+x+%5Cleq+4+%5C%5C+%5C%5Cx+%5Cin+%5B0%2C8%3B+%5C+2%29+%5C%5C+%5C%5C+3%29+%5C+%5C+x+%5Cgeq+2+%5C+%5C+%281%2B%2C+%5C+2%2B%29+%5C%5C+%5C%5C+3x-6%2B5x-4+%5Cleq+10+%5C%5C+8x+%5Cleq+20+%5C%5C+x+%5Cleq+2%2C5+%5C%5C+%5C%5C+x+%5Cin+%5B2%3B+%5C+2%2C5%5D "\boxed 6 \\ \\ \tt 3|x-2|_{(1)}+|5x-4|_{(2)} \leq 10 \\ \\ x-2=0 \ \ \Rightarrow \ \ x=2 \\ 5x-4=0 \ \ \Rightarrow \ \ x=0,8 \\ \\ 1) \ \ x<0,8 \ \ (1-, \ 2-) \\ \\ -3x+6-5x+4 \leq 10 \\ -8x \leq 0 \\ x \geq 0 \\ \\ x \in [0; \ 0,8) \\ \\ 2) \ \ x \in [0,8; \ 2) \ \ (1-, \ 2+) \\ \\ -3x+6+5x-4 \leq 10 \\ 2x \leq8 \\ x \leq 4 \\ \\x \in [0,8; \ 2) \\ \\ 3) \ \ x \geq 2 \ \ (1+, \ 2+) \\ \\ 3x-6+5x-4 \leq 10 \\ 8x \leq 20 \\ x \leq 2,5 \\ \\ x \in [2; \ 2,5]")