Решите систему неравенств
[tex]1) \left \{ {{5(x+1)-x\ \textgreater \ 2x+2} \atop {4(x+1)-2 \leq 2(2x+1)-x} \right.
2) \left \{ {(x+2)(x-6) \leq (x+2)(x+1)+4} \atop {2(6x-1) \geq 7(2x-4)}} \right. [/tex]
[tex]1) \left \{ {{5(x+1)-x\ \textgreater \ 2x+2} \atop {4(x+1)-2 \leq 2(2x+1)-x} \right.
2) \left \{ {(x+2)(x-6) \leq (x+2)(x+1)+4} \atop {2(6x-1) \geq 7(2x-4)}} \right. [/tex]
Answers & Comments
{4(x+1)-2<=2(2x+1)-x
Решим 1 неравенство системы:
5x+5-x>2x+2
4x+5>2x+2
4x-2x>2-5
2x>-3
x=-3/2
Решим 2 неравенство:
4x+4-2<=4x+2-x
4x+2<=3x+2
4x-3x<=2-2
x<=0
Соединим решения двух неравенств:
_________(-3/2)__________________
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___________________[0]__________
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Ответ:x e (-3/2; 0]
2){(x+2)(x-6)<=(x+2)(x+1)+4
{2(6x-1)>=7(2x-4)
Решим 1 неравенство:
x^2-6x+2x-12<=x^2+x+2x+2+4
x^2-4x-12<=x^2+3x+6
x^2-4x-12-x^2-3x-6<=0
-7x-18<=0
-7x<=18
7x>=-18
x>=-18/7
Решим 2 неравенство:
12x-2>=14x-28
12x-14x>=2-28
-2x>=-26
2x<=26
x<=13
Соединим решения двух неравенств:
__________[-18/7]________________
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____________________[13]________
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Ответ:x e [-18/7; 13]