4. 5x − 4 > 7x − 16 y 8 − 7x < 16 − 15x 12 > 2x 8x < 8 6>x x <1 x < 1 Rta 5.
8. ( x − 1)( x + 2) < ( x + 2)( x − 3) y
− 3< x < − 2
120 < 20x 6<x
7.
x−1 x− 5 < x+ 4 x−1
(x − 1) < (x − 5)(x + 4) 2
x 2 + 5x + 6 > x 2 + 6 x − 16 22 > x
x 2 − 2 x + 1< x 2 − x − 20 21< x 21< x < 22
5 x > 20 x>4
4 < x < 6 Rta
EJERCICIO 166 3.
Rta
10. x → Nº s. enteros x y 4x + 8 < 3x + 15 3x − 6 > + 4 2 x<7 6x − 12 > x + 8 5x > 20 x>4 4 < x < 7 Luego son 5 y 6 Rta
x x 2 − 1> − 1 21 y 2x − 3 35 > x + 5 4 3 3x − 12 > 4x − 18 10x − 18 > 5x + 2
x = Ky 1. x = Ky 2. 9 = K6 2 = K3 9 2 =K =K 6 3 3 2 x = ⋅8 24 = y 2 3 x = 12 3 ⋅ 24 =y 2 36 = y
Rta
y
(x + 2)(x + 3) > (x − 2)(x + 8)
2x − 3 < x + 10 y 6x − 4 > 5x + 6 2x − x < 10 + 3 6x − 5x > 6 + 4 x < 13 x > 10 10 < x < 13 Rta
18 − 12 > 4 x − 3x 6>x
x+ 2 x− 2 > x+8 x+3
9.
x > 20 Rta
6.
x 2 + 8 x + 15 > x 2 + 7 x + 12 x> − 3
x<−2
x x 3 − 3 > + 2 y 2x + < 6 x − 23 25 2 4 5 2x − 12 > x + 8 10x + 3 < 30x − 117 x > 20
(x + 3)(x + 5) > (x + 4)(x + 3)
x2 + x − 2 < x2 − x − 6 2x < − 4
A = KBC 30 = K (2)(5) 30 =K 10 3= K A = 3(7)( 4) A = 84
4. x = KYZ
4 = K ( 3)(6)
4 =K 18 2 =K 9 10 = Ky9 2 y9 9 10 = 2 y 5= y
10 =
K B K 3= 5 15 = K
5. A =
K 7 15 A= = 2 71 7 A=
K A 1 K = 3 1 2 1 = 2K 3 1 =K 6 1 1 1 1 = 6 ⇒ = 12 A 12 6A ⇒ 6A = 12 ⇒ A = 2
6. B =
K 11. A → Area del 12. Ap → Area piramide KB K y 9. x = K y 2 − 1 10. x = 2 cuadrado 8. x = y −1 a → apotema C Z 2 → d Diagonal = − K 48 5 1 K → perim. de la b. pb K 12 4K 9= 2 8= 3= 2 Ap = Kapb − 3 1 = A Kd 3 8 48 = K 25 − 1 2 2 8 = 4K m2 = K (12m)(80m) 480 24 = 4 K K 18m = K ( 6m) 48 = 9 =K 2 =K 480m2 = K (960m2 ) 6 =K 8 24 18m2 =K 2⋅7 72 = K 7 ⋅6 480m2 2= K 36m2 A= 10 = =K 14 960m2 Z 72 1 x = 2 72 − 1 x= 2 = K A =1 1 42 5 −1 2 =K Z= x = 2 ⋅ 48 2 10 1 2 72 1 A = (10m) x = 96 x= Z = 4 51 Ap = ( 6m)( 40m) 2 24 2 100m2 x=3 240m2 A= Ap = 2 2 A = 50m2 Ap = 120m2
7. A =
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