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Ответ

Ответ дан
Лексия
1) 5x-3(5x-8)<-7
5x-15x+24<-7
-10x<-7-24
-10x<-31
10x>31
x>3,1
Ответ: X
∈(3,1;+∞)
2) 2 x^{2} -11x+23 textgreater  (x-5) ^{2}  \ 2 x^{2} -11x+23 textgreater   x^{2} -10x+25 \ <br />
 x^{2} -1x-2 textgreater  0 \  D=1-4*(-2)= 3^{2}  \ x1=(1-3):2=-1 \ x2=(1+3):2=2<br />
Ответ: X∈(-∞;-1) ∨ (-1;+∞)
3) 4 x^{2} +10x-20 leq (x+2)^{2} \ 4 x^{2} +10x-20 leq x^{2} +4x+4 \ 3 x^{2}+6x-24 leq 0 \ x^{2} +2x-8 leq 0 \ <br />
D=4-4*(-8)=6^{2}  \ <br />
x1=(-2-6):2=-4 \ <br />
x2=(-2+6):2=2<br />
Ответ: x∈[4;2]
4) x^{2} +8x+15 textless  0 \ <br />
D=64-4*15= 2^{2}  \ <br />
x1=(-8-2):2=-5 \ <br />
x2=(-8+2):2=-3
Ответ: x∈(-5:-3)
5)(x+3)(x-8) geq 0
Ответ: X
∈(-∞:-3]∨[8:+∞)
6) 1+xleq 5x-8<br />
 \ 9 leq 4x \ x geq 2.25<br />
Ответ: x∈[2,25;+∞)
7)  x^{2} -32x leq 0 \ x(x-32) leq 0 \ x=0 \   x-32=0 \ <br />
x=32
Ответ: X∈[0;32]
8) x^{2} -36 textgreater  0 \ <br />
 x^{2}  textgreater  36 \ <br />
x1=6 \ <br />
x2=-6<br />
Ответ: X∈(-∞;-6)∨(6:+∞)
9) x^{2} -7x+12 geq 0 \ D=49-4*12=1 \  x1=(7-1):2=3 \ x2=(7+1):2=4
Ответ: X∈(-∞:3]∨[4:+∞)
10) 22-x>5-4(x-2)
22-x>5-4x+8
3x>-9
x>3
Ответ: X∈(3;+∞)
11) 5x+8 geq -3x
8x geq -8
x geq -1
Ответ: x∈[-1;+∞)
12) 3x-6 leq 0
3x leq 6
x leq 2
Ответ: x∈(-∞:2]

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