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DSA4SA
@DSA4SA
October 2021
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Помогите, пожалуйста, решить неравенства:
1)(-3x-2)(6-x)(4x+1)<0
2) (1-2x)(2x-3)(5x-2)<0
3)(-2x-3)(x-1)x(5x-4)<0
4)(-x-2)(1-x)(5x+2)>0
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sedinalana
Verified answer
1)(-3x-2)(6-x)(4x+1)<0
(3x+2)(x-6)(4x+1)<0
x=-2/3 x=6 x=-1/4
_ + _ +
--------------(-2/3)----------(-1/4)---------(6)--------------
x∈(-∞;-2/3) U (-1/4;6)
-
2) (1-2x)(2x-3)(5x-2)<0
x=0,5 x=1,5 x=0,4
+ _ + _
----------(0,4)----------(0,5)----------(1,5)-----------
x∈(0,4;0,5) U (1,5;∞)
3)(-2x-3)(x-1)x(5x-4)<0
(2x+3)(x-1)x(5x-4)>0
x=-1,5 x=1 x=0 x=0,8
+ _ + _ +
-------------(-1,5)-----------(0)-----------(0,8)------------(1)------------------
x∈(-∞;-1,5) U (0;0,8) U (1;∞)
4)(-x-2)(1-x)(5x+2)>0
(x+2)(x-1)x(5x+2)>0
x=-2 x=1 x=0 x=-0,4
+ _ + _ +
---------(-2)-----------(-0,4)----------(0)------------(1)------------------
x∈(-∞;-2) U (-0,4;0) U (1;∞)
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Answers & Comments
Verified answer
1)(-3x-2)(6-x)(4x+1)<0(3x+2)(x-6)(4x+1)<0
x=-2/3 x=6 x=-1/4
_ + _ +
--------------(-2/3)----------(-1/4)---------(6)--------------
x∈(-∞;-2/3) U (-1/4;6)
-
2) (1-2x)(2x-3)(5x-2)<0
x=0,5 x=1,5 x=0,4
+ _ + _
----------(0,4)----------(0,5)----------(1,5)-----------
x∈(0,4;0,5) U (1,5;∞)
3)(-2x-3)(x-1)x(5x-4)<0
(2x+3)(x-1)x(5x-4)>0
x=-1,5 x=1 x=0 x=0,8
+ _ + _ +
-------------(-1,5)-----------(0)-----------(0,8)------------(1)------------------
x∈(-∞;-1,5) U (0;0,8) U (1;∞)
4)(-x-2)(1-x)(5x+2)>0
(x+2)(x-1)x(5x+2)>0
x=-2 x=1 x=0 x=-0,4
+ _ + _ +
---------(-2)-----------(-0,4)----------(0)------------(1)------------------
x∈(-∞;-2) U (-0,4;0) U (1;∞)