1) Completa el siguiente cuadro
2) Resolver las siguientes desigualdades, expresar la solución como intervalo y en la recta numérica.
a) 3/x≥3
Caso 1
x>0
3≥3x
3/3≥x
1≥ x
x≤1
x>0 ∩ x≤1
c.s. (0,1]
caso 2
x<0
3/x≤3
3≤3x
3/3≤x
x≥1
x<0 ∩ x≥1
c.s. (0)
b) 5/x < 6/7
Caso 1
x > 0
5 < 6/7 x
5/1 / 6/7 < x
x > 35/6
x > 1 ∩ x > 35/6
c.s. (35/6, ∞)
caso 2
x < 0
5 > 6/7 x
5/1 / 6/7 > x
x < 35/6
x < 0 ∩ x<35/6
c.s. (-∞, 0)
c) x/ 2-4x ≤ 5/6
caso 1
2x - 4 > 0
2x > 4
x >2
x ≤ 5/6 (2-4x)
6(x ≤ 10/6- 20/6x
6x ≤ 10 – 20x
26x ≤ 10
x ≤ 10/26
x ≤5/13
x > 0 ∩ x ≤ 5/13
c.s. ( Ø )
Caso 2
x < 2
x ≥ 5/6(2-4x)
6( x ≥ 10/6- 20/6x)
6x ≥ 10-20x
26x ≥ 10
x ≥ 10/26
x ≥ 5/13
x < 2 ∩ x ≥ 5/13
d) x/2x-3 > 5
caso 1
2x-3 >0
x > 3/2
x > 5(2x-3)
x > 10x-15
x-10x > -15
-1(-9x > -15)
9x < 15
x < 15/9
x < 5/3
x > 3/2 ∩ x < 5/3
c.s. (3/2, 5/3)
Caso2
2x-3<0
x<3/2
x<5(2x-3)
x<10x-15
-1(-9x<-15)
9x > 15
x> 5/3
x<3/2 ∩ x> 5/3
c.s. (Ø)
c.s. (Ø) u (3/2, 5/3)
e) -1< 3-7x/4 ≤ 6
-3-4 <-7x ≤ 24-3
-1 (-7<-7x ≤ 21)
(7>7x ≥ -21)/ 7
1 >x ≥-3
c.s [-3, 1)
Tarea 3
1.- |7-3x/2| ≤ 1
Caso 1
2 ( 7-3x/2 ≤ 1)
7-3x ≤ 2
-1(-3x ≤ 2-7)
3x ≥ 5
X ≥ 5/3
c.s. [5/3, ∞)
Caso 2
(7-3x/2 ≥ -1 ) 2
(-3x ≥-2-7) -1
3x ≤ 9
X ≤ 9/3
X ≤ 3
c.s.(-∞, 3 ]
(-∞, 3 ] n [5/3, ∞)
c.s. [5/3, 3]
2.- |1-2x/3 | < 4
-4<1-2x/3<4
(-5<-2x/3<3)3
-1(-15<-2x<9)
15/2>x>-9/2
c.s (-9/2, 15/2)
3.- |3-11x| ≥ 41
Caso1
3-11x ≥41
-1(-11x≥ 41-3)
11x ≤ 38
X ≤38/11
c.s. (-∞, -38/11]
caso2
3-11x≤-41
-1(-11x≤-41-3)
11x≥44
x≥ 4
c.s. [4, ∞)
c.s. (-∞, 38/11] u [4,∞ )
