EJERCICIOS DE REEMPLAZO PARA EL 8 DE MARZO

1. 10-5x/2>=0
20-5x/2 >=
20/2 >= 5x/2
20(2)/2 >=5x
20/5>=x
4>=x
Intervalo: [4, inf)

4. (x-1)(x+2)<(x+1)(x-3)
x^2+2x-x-2 < x^2-3x+x-3
x^2+x-2 < x^2-2x-3
x-2+2x+3<0
3x+1<0
3x<1
x<-1/3
x<-0,3
Intervalo: (-inf, -0,3)

17. 1/x-x/2x-1 >=1
2x-1-(x)(x)/(x)(2x-1) >=1
2x-1-x^2/2x^2-1x >=1
2x-1-x^2 >= 2x^2-1x
2x-1-x^2-2x^2-1X >=0
2x-3x^2-1x-1 >= 0
x-3x^2-1 >= 0
3x^2+x-1 >=0
a b c

x= -1+- raiz de 1^2-4(-3)(-1)
-1+- raiz de 1-12/-6
-1+- raiz de -11/-6

NO TIENE SOLUCIÒN

20. 2-x/x-3<=-2/x
x(2-x) <=-2(x-3)
2x-x^2<=-2x+6
2x-x^2+2x-6<=0
-x^2+4x-6<=0
0<=x^2-4x+6

x= -4+-raiz de 4^2-4(1)(6)/2(1)
-4+- raiz de 16+24/2
-4+- raiz de 40/2
-4+- 6,3/2

1. -4+6,3/2
2,3/2
1,15
2. -4-6,3/2
-10,3/2
-5,15
Intervalos: (-inf, -5,15] u [1,15 , inf)

21. 2x/1-2x <=3-x/x
(2x)(x) <=(1-2x)(3-x)
2x^2 <= 3-x-6x+2x^2
0<=3-x-6x
0<=3-7x
-3<=-7x
-3/-7<=x
0,4<=x
Intervalo: [0,4 , inf)

22. x^3/x^2+3x-4 >=x
x^3 >=(x^2+3x-4)(x)
x^3 >=x^3+3x^2-4x
0>=3x^2-4x

x= -4+- raiz de 4^2-4(3)(0)/2(3)
-4+- raiz de 16-0/6
-4+- raiz de 16/6

1. -4+4/6
0
2. -4-4/6
8/6
-1,3
Intervalo: [-1,3 , 0]

26. -2/3+x >=x/4-x
(-2)(4-x) >= (x)(3+x)
-8+2x >= 3x+x^2
0>=3x+x^2+8-2x
0>=x+x^2+8
0>=x^2+x+8

x= -1+- raiz de 1^2-4(1)(8)/2(1)
-1+- raiz de 1-32/2
-1+- raiz de -31/2
NO TIENE SOLUCIÓN

27. x/x-1 >= 5/4+2x
(x)(4+2x) >= (5)(x-1)
4x+2x^2 >= 5x-5
4x+2x^2-5x+5>=0
x+2x^2+5>=0
2x^2+x+5 >=0
x= -1+- raiz de 1^2-4(2)(5)/2(2)
-1+- raiz de 1-40/4
-1+- raiz de -39/4
NO TIENE SOLUCIÓN

29. x-2/x+2 < 1+x/x-1
(x-2)(x-1)<(1+x)(x+2)
x^2+x-2x+2 x^2-x+2<3x+2+x^2
-3x<0
-x-3x<0
-4x<0
x<1/-4
x<-0,25
Intervalo: (-inf , -0,25)

33. 3+x <= x^2-1/x-1
(3+x)(x-1)<=(x^2-1)
3x-3+x^2-x<= x^2-1
2x-3+x^2<= x^2-1
2x-3+1<=0
2x-2<=0
2x<=2
x<=2/2
x<=1
Intervalo: (-inf , 1]