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REPUBLICA BOLIVARIANA DE VENEZUELA
MINISTERIO DEL PODER POPULAR PARA LA EDUCACION SUPERIOR
UNIVERSIDAD POLITECNICA TERRITORIAL ANDRES ELOY BLANCO
EXTENSION BARQUISIMETO- ESTADO LARA
Estudiante:
Oriana Pérez
CI:25992499
Es una agrupación de elementos que posee una o varias características en
común .
Un conjunto es representado por una letra mayúscula, encerrándose sus
elementos, separados por comas, entre llaves. Por ejemplo, el conjunto A,
integrado por las vocales, se representaría así: A= {a, e, i, o, u}.
Ejercicio:
A= 1,2,3,4,5,6
B= 2,4,6,8,10
C= 5,6,7,8,9
Calcular
a) (A ∪ 𝐵) ∩ 𝐶
b) (B ∩ 𝐶) ∪ (𝐴 ∩ 𝐵)
a) A ∪ 𝐵 = 1,2,3,4,5,6,8,10
𝐶 = 5,6,7,8,9
(A ∪ 𝑩) ∩ 𝑪= 5,6,8
b) B ∩ 𝐶 = 𝟔, 𝟖
𝐴 ∩ 𝐵 = 𝟐, 𝟒, 𝟔
(B ∩ 𝐶) ∪ (𝐴 ∩ 𝐵) = 2,4,6,8
𝒃) 𝟕 − 𝟐
𝟐
=
= 𝟕
𝟐
- 2 𝟕. 𝟐+ 𝟐
𝟐
= 7 - 2 𝟏𝟒 + 2
=9 -2 𝟏𝟒
a) 6. −𝟑. −𝟓 + 𝟒 + 𝟔 =
= 6. −𝟑. −𝟏 + 𝟔
=6. 𝟑 + 𝟔
=6.9
=54
𝑎) 4𝑥 + 5 > 2𝑥 + 9 =
=4𝑥 − 2𝑥 > 9 − 5
=2𝑥 > 4
=𝑥 >
4
2
=𝑥 > 2 +∞
−∞
0 4
1 3
2
-1
-4 -2
-3
b) 2𝑥 + 7 ≤ 5𝑥 − 8 =
=2𝑥 − 5𝑥 ≤ −8 − 7
=−3𝑥 ≤ −15
=𝑥 ≥
−15
−3
=𝑥 ≥ 5
+∞
−∞
0 4
2 6 8 10
-2
-4
-6
-8
-10
El valor absoluto de un número es su valor numérico sin tener en cuenta su
signo ya sea este positivo o negativo.
𝒂) 𝟕 − 𝟐𝒙 ≥ 𝒙 − 𝟑 =
Debe cumplirse alguna de las 2 inecuaciones:
𝒂) 𝟕 − 𝟐𝒙 ≥ 𝒙 − 𝟑 ∪ 𝑏)7 − 2𝑥 ≤ − 𝑥 − 3
Resolvemos:
𝒂) 𝟕 − 𝟐𝒙 ≥ 𝒙 − 𝟑
=7 + 3 ≥ 𝑥 + 2𝑥
=10 ≥ 3𝑥
=𝑥 ≤
1𝑜
3
𝑏)7 − 2𝑥 ≤ − 𝑥 − 3
=7 − 2𝑥 ≤ −𝑥 + 3
=7 − 3 ≤ −𝑥 + 2𝑥
=4 ≤ 𝑥
+∞
−∞
0 4
2 6 8 10
-2
-4
-6
-8
-10
b) 𝟕 − 𝟐𝒙 ≥ 𝒙 − 𝟑 =
Debe cumplirse alguna de las 2 inecuaciones:
𝒂)𝟐𝒙 − 𝟏 ≤ − 𝟑 − 𝟏 ∪ 𝒃)𝟐𝒙 − 𝟏 ≥ 𝒙 − 𝟑
Resolvemos:
𝒂)𝟐𝒙 − 𝟏 ≤ − 𝟑 − 𝒙 =
=2𝑥 − 1 ≤ −3 + 𝑥
=2𝑥 − 𝑥 ≤ −3 + 1
=𝑥 ≤ −2
𝒃)𝟐𝒙 − 𝟏 ≥ 𝒙 − 𝟑
=2𝑥 + 𝑥 ≥ 3 + 1
=3𝑥 ≥ 4
=𝑥 ≥
4
3
+∞
−∞
0 4
2 6 8 10
-2
-4
-6
-8
-10

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Matematica

  • 1. REPUBLICA BOLIVARIANA DE VENEZUELA MINISTERIO DEL PODER POPULAR PARA LA EDUCACION SUPERIOR UNIVERSIDAD POLITECNICA TERRITORIAL ANDRES ELOY BLANCO EXTENSION BARQUISIMETO- ESTADO LARA Estudiante: Oriana Pérez CI:25992499
  • 2. Es una agrupación de elementos que posee una o varias características en común . Un conjunto es representado por una letra mayúscula, encerrándose sus elementos, separados por comas, entre llaves. Por ejemplo, el conjunto A, integrado por las vocales, se representaría así: A= {a, e, i, o, u}.
  • 3. Ejercicio: A= 1,2,3,4,5,6 B= 2,4,6,8,10 C= 5,6,7,8,9 Calcular a) (A ∪ 𝐵) ∩ 𝐶 b) (B ∩ 𝐶) ∪ (𝐴 ∩ 𝐵) a) A ∪ 𝐵 = 1,2,3,4,5,6,8,10 𝐶 = 5,6,7,8,9 (A ∪ 𝑩) ∩ 𝑪= 5,6,8 b) B ∩ 𝐶 = 𝟔, 𝟖 𝐴 ∩ 𝐵 = 𝟐, 𝟒, 𝟔 (B ∩ 𝐶) ∪ (𝐴 ∩ 𝐵) = 2,4,6,8
  • 4. 𝒃) 𝟕 − 𝟐 𝟐 = = 𝟕 𝟐 - 2 𝟕. 𝟐+ 𝟐 𝟐 = 7 - 2 𝟏𝟒 + 2 =9 -2 𝟏𝟒 a) 6. −𝟑. −𝟓 + 𝟒 + 𝟔 = = 6. −𝟑. −𝟏 + 𝟔 =6. 𝟑 + 𝟔 =6.9 =54
  • 5. 𝑎) 4𝑥 + 5 > 2𝑥 + 9 = =4𝑥 − 2𝑥 > 9 − 5 =2𝑥 > 4 =𝑥 > 4 2 =𝑥 > 2 +∞ −∞ 0 4 1 3 2 -1 -4 -2 -3 b) 2𝑥 + 7 ≤ 5𝑥 − 8 = =2𝑥 − 5𝑥 ≤ −8 − 7 =−3𝑥 ≤ −15 =𝑥 ≥ −15 −3 =𝑥 ≥ 5 +∞ −∞ 0 4 2 6 8 10 -2 -4 -6 -8 -10
  • 6. El valor absoluto de un número es su valor numérico sin tener en cuenta su signo ya sea este positivo o negativo.
  • 7. 𝒂) 𝟕 − 𝟐𝒙 ≥ 𝒙 − 𝟑 = Debe cumplirse alguna de las 2 inecuaciones: 𝒂) 𝟕 − 𝟐𝒙 ≥ 𝒙 − 𝟑 ∪ 𝑏)7 − 2𝑥 ≤ − 𝑥 − 3 Resolvemos: 𝒂) 𝟕 − 𝟐𝒙 ≥ 𝒙 − 𝟑 =7 + 3 ≥ 𝑥 + 2𝑥 =10 ≥ 3𝑥 =𝑥 ≤ 1𝑜 3 𝑏)7 − 2𝑥 ≤ − 𝑥 − 3 =7 − 2𝑥 ≤ −𝑥 + 3 =7 − 3 ≤ −𝑥 + 2𝑥 =4 ≤ 𝑥 +∞ −∞ 0 4 2 6 8 10 -2 -4 -6 -8 -10
  • 8. b) 𝟕 − 𝟐𝒙 ≥ 𝒙 − 𝟑 = Debe cumplirse alguna de las 2 inecuaciones: 𝒂)𝟐𝒙 − 𝟏 ≤ − 𝟑 − 𝟏 ∪ 𝒃)𝟐𝒙 − 𝟏 ≥ 𝒙 − 𝟑 Resolvemos: 𝒂)𝟐𝒙 − 𝟏 ≤ − 𝟑 − 𝒙 = =2𝑥 − 1 ≤ −3 + 𝑥 =2𝑥 − 𝑥 ≤ −3 + 1 =𝑥 ≤ −2 𝒃)𝟐𝒙 − 𝟏 ≥ 𝒙 − 𝟑 =2𝑥 + 𝑥 ≥ 3 + 1 =3𝑥 ≥ 4 =𝑥 ≥ 4 3 +∞ −∞ 0 4 2 6 8 10 -2 -4 -6 -8 -10