Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 361]
Code Context
                $n = array_keys($lista,$lecture["Lecture"]["id"]);

                if($n[0]-1 == 0){
$playlist	=	array(
	"Playlist" => array(
	"id" => "4",
	"name" => "Álgebra",
	"slug" => "algebra",
	"number" => "2",
	"description" => "Rama que estudia las reglas de las expresiones y ecuaciones con variables.",
	"lateral" => "1",
	"image" => "wE6OydOzC-k",
	"index" => "0"
),
	"Lecture" => array(
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)
)
$video	=	array(
	"Video" => array(
	"id" => "115",
	"name" => "Determinantes (sistemas lineales 3x3)",
	"youtube" => "sS-vy-es0j0",
	"slug" => "determinantes-sistemas-lineales-3x3",
	"date" => "2014-10-06 02:08:12",
	"mp4" => "https://dl-web.dropbox.com/get/Videos_math2me_mp4_480p/%C3%81lgebra_m2m_480p/Cap%C3%ADtulo%20IX.%20Ecuaciones%20simult%C3%A1neas%20lineales%203x3/Determinantes%20(sistemas%20lineales%203x3).mp4?_subject_uid=70082452&w=AADs7k-YnAc7pwrPEELB3a488H6qRLm5HfLLj0QtJZqPVg&dl=1",
	"flv" => "",
	"exercise" => "",
	"words" => ""
),
	"Lecture" => array()
)
$time_start	=	1503250114.04
$vID	=	"115"
$params_p	=	array(
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),
	"order" => array(
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)
)
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),
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)
$lecture	=	false
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$positions	=	array(
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),
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)
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),
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)
)
$id	=	"4"
$title	=	"Determinantes (sistemas lineales 3x3) @ math2me.com"
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	"order" => "Lecture.id DESC",
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)
)
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PlaylistController::video() - APP/Controller/PlaylistController.php, line 361
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 364]
Code Context
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PlaylistController::video() - APP/Controller/PlaylistController.php, line 364
ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  -1 [APP/Controller/PlaylistController.php, line 364]
Code Context
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ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 366]
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ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
Dispatcher::dispatch() - CORE/Cake/Routing/Dispatcher.php, line 89
[main] - APP/webroot/index.php, line 96

Notice (8): Undefined offset:  0 [APP/Controller/PlaylistController.php, line 369]
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ReflectionMethod::invokeArgs() - [internal], line ??
Controller::invokeAction() - CORE/Cake/Controller/Controller.php, line 473
Dispatcher::_invoke() - CORE/Cake/Routing/Dispatcher.php, line 107
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Determinantes (sistemas lineales 3x3) [

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/331]

---

Álgebra

I. Traducción de expresiones algebraicas

• 1. Traducción de lenguaje común a algebraico
• 2. Traducir lenguaje común a algebraico│ejercicio 1
• 3. Traducir lenguaje común a algebraico│ejercicio 2
• 4. Traducir un enunciado a expresión matemática
• 5. Traducción de lenguaje algebraico a común
• 6. Traducir lenguaje algebraico a común│compilado
• 7. Ejercicio de traducir una ecuación a un lenguaje verbal
• 8. Traducción + Interpretación = Ecuación
• 9. Sustituir valores en una expresión algebraica│ejercicio 1
• 10. Sustituir valores en una expresión algebraica│ejercicio 2
• 11. Sustituir valores en una expresión algebraica│ejercicio 3
• 12. Sustituir valores en una expresión algebraica│ejercicio 4

II. Razones y proporciones

• 13. Concepto de razón
• 14. Razones│ejercicio 1
• 15. Razones│ejercicio 2
• 16. Concepto de proporción
• 17. Propiedades de las proporciones
• 18. Proporciones│ ejercicio 1
• 19. Proporciones│ejercicio 2
• 20. Proporciones│ejercicios
• 21. Regla de tres simple
• 22. Regla de tres simple│ejercicio 1
• 23. Regla de tres simple│ejercicio 2
• 24. Regla de tres simple│ejercicio 3
• 25. Regla de tres simple│ejercicio 4
• 26. Regla de tres simple│ejercicio 5
• 27. Regla de tres simple│ejercicio 6
• 28. Intro a la regla de tres simple│directa e inversa
• 29. Regla de tres simple │variación inversa 1
• 30. Regla de tres simple│directas e inversas
• 31. Regla de tres simple│variación directa
• 32. Regla de tres simple│variación inversa 1
• 33. Regla de tres simple│variación inversa 2
• 34. Regla de tres simple│mixtas
• 35. Porcentajes
• 36. Porcentajes│ejercicio 1
• 37. Porcentajes│ejercicio 2
• 38. Porcentajes│ejercicio 3

III. Polinomios

• 39. Conceptos importantes de los polinomios
• 40. Identificar el concepto de polinomio
• 41. Identificar el uso de un exponente en un monomio
• 42. Términos y Polinomios
• 43. Reducir términos semejantes│ejercicio 1
• 44. Reducir términos semejantes│ejercicio 2
• 45. Reducir términos semejantes - ejercicio 3
• 46. Reducir términos semejantes│ejercicio 4
• 47. Reducir términos semejantes│ejercicio 5
• 48. Reducir términos semejantes│ejercicio 6
• 49. Reducir términos semejantes│ejercicio 7
• 50. Reducir términos semejantes│ejercicio 8
• 51. Reducir términos semejantes│compilado
• 52. Reducir términos semejantes con fracciones│ej. 1
• 53. Reducir términos semejantes│problema 1
• 54. Suma y resta de polinomios
• 55. Suma de expresiones algebraicas
• 56. Suma de expresiones algebraicas │ fracciones
• 57. Signos de agrupación en polinomios
• 58. Reducir términos con parentésis│ejercicio 1
• 59. Reducir términos con parentésis│ejercicio 2
• 60. Reducir términos con parentésis│ejercicio 3
• 61. Reducir términos con parentésis│ejercicio 4
• 62. Reducir términos con parentésis│ejercicio 5
• 63. Reducir términos con parentésis│ejercicio 6
• 64. Reducir términos con parentésis│ejercicio 7
• 65. Leyes de los Exponentes - Versión Final
• 66. Leyes de los exponentes
• 67. Leyes de los exponentes│ejercicio 1
• 68. Leyes de los exponentes│ejercicio 2
• 69. Leyes de los exponentes│ejercicio 3
• 70. Leyes de los exponentes│ejercicio 4
• 71. Leyes de los exponentes│ejercicio 5
• 72. Leyes de los exponentes│ejercicio 6
• 73. Leyes de los exponentes│ejercicio 7
• 74. Leyes de los exponentes│ejercicio 8
• 75. Leyes de los exponentes│ejercicio 9
• 76. Leyes de los exponentes│ejercicio 10
• 77. Leyes de los exponentes│ejercicio 11
• 78. Leyes de los exponentes│compilado
• 79. Multiplicación de polinomios
• 80. Multiplicación de Polinomios
• 81. Multiplicación de polinomios│ejercicio 1
• 82. Multiplicación de polinomios│ejercicio 2
• 83. Multiplicación de polinomios│ejercicio 3
• 84. Multiplicación de polinomios│ejercicio 4
• 85. Multiplicación de polinomios│ejercicio 5
• 86. Multiplicación de polinomios│ejercicio 6
• 87. Multiplicación de polinomios│ejercicio 7
• 88. Multiplicación de polinomios│ejercicio 8
• 89. Multiplicación de polinomios│problema 1
• 90. Multiplicación de polinomios│problema 2
• 91. División de polinomios
• 92. División de polinomios│ejercicio 1
• 93. División de polinomios│ejercicio 2
• 94. División de polinomios│ejercicio 3
• 95. Leyes de los exponentes │ División │ ejercicio 1
• 96. División de polinomios│ejercicio 4
• 97. División de operaciones con paréntesis│ejercicio 1
• 98. Fracciones combinadas con X │ejercicio 1

IV. Productos notables

• 99. ✅ Explicación de un Binomio con término común │ Productos notables
• 100. Binomios conjugados - productos notables
• 101. Binomios conjugados│ejercicio 1
• 102. Binomios conjugados│raíz cuadrada│ej 1
• 103. Binomios conjugados│raíz cuadrada│ej 2
• 104. Binomios conjugados│raíz cuadrada│ej 3
• 105. Binomios conjugados│raíz cuadrada│ej 4
• 106. Binomio al cuadrado
• 107. Binomio al cuadrado│ejercicio 1
• 108. Binomio al cuadrado│ejercicio 2
• 109. Binomio al cuadrado│ejercicio 3
• 110. Binomio al cuadrado│ejercicio 4
• 111. Binomio con exponente negativo
• 112. Binomio al cuadrado con fracciones
• 113. Binomio al cuadrado con fracciones│ejercicio 1
• 114. Identificar a un binomio al cuadrado
• 115. Ejercicio para desarrollar un binomio al cuadrado
• 116. Binomio al cubo
• 117. Binomio al cubo │ejercicio 1
• 118. Binomio a la cuarta
• 119. Binomio a la cuarta│ejercicio 1
• 120. Productos notables - completo
• 121. Productos notables │ binomios con término común
• 122. Productos notables│ejercicio 1
• 123. Productos notables│problema 1
• 124. Triángulo de Pascal y binomio de Newton
• 125. Binomio al CUBO │ Productos Notables
• 126. Binomio al cuadrado │ tres términos

V. Factorización

• 127. Métodos de factorización
• 128. Factorización por factor común
• 129. Factorización por factor común con fracciones
• 130. Factorización por factor común│ejercicio 1
• 131. Factorización por factor común│ejercicio 2
• 132. Factorización por factor común│ejercicio 3
• 133. Diferencia de cuadrados │ factorización
• 134. Factorización por diferencia de cuadrados│ej 1
• 135. Factorización por diferencia de cuadrados│ej 2
• 136. Factorización por diferencia de cuadrados│ej 3
• 137. Diferencia de cuadrados│problema 1
• 138. Factorización de un trinomio x²+bx+c
• 139. Factorización de un trinomio │ x²+bx+c
• 140. Factorización de un trinomio x²+bx+c│ejercicio 1
• 141. Factorización de un trinomio x²+bx+c│ejercicio 2
• 142. Factorización de un trinomio x²+bx+c│problema 1
• 143. Factorización de un trinomio ax²+bx+c
• 144. Factorización de un trinomio │ ax²+bx+c
• 145. Factorización de un trinomio ax²+bx+c│ejercicio 1
• 146. Factorización de un trinomio cuadrado perfecto
• 147. Factorizar un trinomio cuadrado perfecto con fracciones
• 148. Factorización de una suma de cubos (x³ + y³)
• 149. Factorización de una diferencia de cubos (x³ - y³)
• 150. Factorización por agrupación
• 151. Factorización por agrupación│ejercicio 1
• 152. Factorización por agrupación│ejercicio 2
• 153. Factorización de un trinomio cuadrado perfecto │ ejercicio 1

VI. Expresiones racionales

• 154. Simplificacion de fracciones algebraicas│ej 1 al 4
• 155. Simplificacion de fracciones algebraicas│ej 5 al 7
• 156. Simplificacion de fracciones algebraicas│ej 8
• 157. Simplificacion de fracciones algebraicas│ej 9
• 158. Simplificacion de fracciones algebraicas│ej 10
• 159. Simplificacion de fracciones algebraicas│ej 11
• 160. Simplificacion de fracciones algebraicas│ej 12
• 161. Expresión equivalente de una fracción algebraica
• 162. Suma de fracciones algebraicas│mismo denominador
• 163. Suma de fracciones algebraicas│ejercicio 1
• 164. Suma de fracciones algebraicas│ejercicio 2
• 165. Suma de fracciones algebraicas
• 166. Multiplicación de fracciones algebraicas
• 167. División de fracciones algebraicas
• 168. División de fracciones algebraicas│ejercicio 1
• 169. División de fracciones algebraicas│ejercicio 2
• 170. División de fracciones algebraicas │ejercicio 3

VII. Ecuaciones lineales

• 171. Concepto de ecuación
• 172. Identificar un elemento de una ecuación
• 173. Propiedades de transposición en una ecuación
• 174. Plantear una ecuación de primer grado│ejercicio 1
• 175. Plantear una ecuación de primer grado│ejercicio 2
• 176. Plantear una ecuación de primer grado│ejercicio 3
• 177. Principio de una ecuación lineal│ejercicio 1
• 178. Principio de una ecuación lineal│ejercicio 2
• 179. Despeje de una variable
• 180. Como DESPEJAR una variable │ ejercicio 1
• 181. Despeje de una variable│ejercicio 1
• 182. Despeje de una variable │ejercicio 2
• 183. Despeje de una variable│ejercicio 4
• 184. Despeje de una variable│ejercicio 3
• 185. Introducción a las ecuaciones de primer grado
• 186. Ecuaciones de primer grado
• 187. Ecuaciones de primer grado con paréntesis
• 188. Ecuaciones de primer grado con fracciones
• 189. Graficar funciones lineales
• 190. Graficar funciones lineales│ejercicio 1
• 191. Ecuaciones de primer grado│ejercicio 1
• 192. Ecuaciones de primer grado con fracciones│ej 1
• 193. Ecuaciones de primer grado con fracciones│ej 2
• 194. Ecuaciones de primer grado con fracciones│ej 3
• 195. Ecuaciones de primer grado con fracciones│ej 4
• 196. Ecuaciones de primer grado con fracciones│transposición
• 197. Plantear y resolver problemas de ecuaciones lineales
• 198. Ecuaciones de primer grado│problema 1
• 199. Ecuaciones de primer grado│problema 2
• 200. Ecuaciones de primer grado│problema 3
• 201. Ecuaciones de primer grado│problema 4
• 202. Ecuaciones de primer grado│problema 5
• 203. Ecuaciones de primer grado con fracciones│problema 1
• 204. Ecuaciones de primer grado con fracciones│problema 2
• 205. Ecuaciones de primer grado con fracciones│problema 3
• 206. Ecuaciones de primer grado con fracciones│problema 4
• 207. Ecuaciones de primer grado con fracciones│problema 5
• 208. Ecuaciones de primer grado con fracciones│problema 6
• 209. Ecuaciones de primer grado con fracciones│problema 7
• 210. Resolver una proporción de fracciones algebraicas
• 211. Ejercicios de ecuaciones de primer grado│compilado 1
• 212. Ejercicios de ecuaciones de primer grado│compilado 2
• 213. Convertir grados Fahrenheit a Centígrados

VIII. Ecuaciones simultáneas lineales 2x2

• 214. Intro a las ecuaciones simultáneas lineales 2x2
• 215. Plantear un sistema de ecuaciones 2x2
• 216. Identificar el método utilizado en un sistema 2x2
• 217. Convertir un sistema lineal 2x2 de fracciones a enteros
• 218. Sistema de ecuaciones lineales 2x2 │ Reducción
• 219. Sistemas de ecuaciones 2x2│método de eliminación 1
• 220. Sistemas de ecuaciones 2x2│método de eliminación 2
• 221. Sistemas de ecuaciones 2x2│método de eliminación 3
• 222. Sistemas 2x2 por método de eliminación│prob 1
• 223. Sistemas 2x2 por método de eliminación│prob 2
• 224. Sistemas 2x2 por método de eliminación│prob 3
• 225. Sistemas de ecuaciones 2x2 │ método de redución │ prob 4
• 226. Sistemas de ecuaciones 2x2│método de sustitución
• 227. Sistemas de ecuaciones 2x2│método de sustitución│prob 1
• 228. Sistemas de ecuaciones 2x2│método de sustitución│prob 2
• 229. Sistemas de ecuaciones 2x2│método de sustitución│prob 3
• 230. Sistemas de ecuaciones 2x2│método de sustitución│prob 4
• 231. Sistemas de ecuaciones 2x2│método de sustitución│prob 5
• 232. Sistemas de ecuaciones 2x2│método de sustitución│prob 6
• 233. Sistemas de ecuaciones 2x2│método de sustitución│prob 7
• 234. Sistemas de ecuaciones 2x2│método de igualación
• 235. Sistemas de ecuaciones 2x2│método de gráfico
• 236. Sistemas de ecuaciones 2x2│método de gráfico especial
• 237. Sistemas de ecuaciones 2x2│método de gráfico│problema
• 238. Sistemas de ecuaciones 2x2│método de gráfico│ejercicio
• 239. Sistemas de ecuaciones 2x2│método por determinantes
• 240. Problemas que generan un sistema de ecuaciones 2x2

IX. Ecuaciones simultáneas lineales 3x3

• 241. Sistemas de ecuaciones 3x3│método por determinantes
• 242. Sistemas de ecuaciones 3x3│método de eliminación
• 243. Sistemas de ecuaciones 3x3│método de igualación
• 244. Obtener un determinante de un sistema 3x3
• 245. Hallar un determinante de un sistema 3x3
• 246. Aplicación de los sistemas lineales 3x3

X. Ecuaciones cuadráticas

• 247. Tipos de ecuaciones cuadráticas│pura, mixta, completa
• 248. Intro a las ecuaciones cuadráticas│segundo grado
• 249. Discriminante de una ecuación cuadrática
• 250. Discriminante de una ecuación cuadrática│ejercicio 1
• 251. Discriminante de una ecuación cuadrática│ejercicio 2
• 252. Discriminante de una ecuación cuadrática│ejercicio 3
• 253. Intersecciones de una ecuación cuadrática│corto
• 254. ¿Por qué una ecuación cuadrática se iguala a cero?
• 255. Ecuaciones cuadráticas puras
• 256. Ecuaciones cuadráticas puras│ejercicio 1
• 257. Ecuaciones cuadráticas mixtas│compilado 1
• 258. Ecuaciones cuadráticas mixtas│compilado 2
• 259. Ecuaciones cuadráticas mixtas con fracciones
• 260. Ecuaciones cuadráticas completas
• 261. Identificar una ecuación cuadrática completa
• 262. Ecuaciones cuadráticas completas│ejercicio 1
• 263. Demostración de la fórmula general
• 264. Sustituir valores en la formula general
• 265. Ecuaciones cuadráticas por fórmula general
• 266. Ecuaciones cuadráticas por fórmula general│ej 1
• 267. Ecuaciones cuadráticas por fórmula general│ej 2
• 268. Radicalizar el resultado de una fórmula general
• 269. Ecuaciones cuadráticas con fracciones
• 270. Factorizar siempre un trinomio ax^2+bx+c
• 271. Hallar la ecuación cuadrática│dadas sus raíces
• 272. Ecuaciones cuadráticas por factorización│ej 1
• 273. Ecuaciones cuadráticas por factorización│ej 2
• 274. Ecuaciones cuadráticas por factorización│compilado
• 275. Ecuaciones cuadráticas completando el TCP│ej 1
• 276. Ecuaciones cuadráticas completando el TCP│ej 2
• 277. Número de intersecciones de una ecuación cuadrática│largo
• 278. Ecuaciones cuadráticas por método de gráfico
• 279. Ecuaciones cuadráticas por método de gráfico│problema 1
• 280. Aplicación de la función cuadrática
• 281. Ecuaciones cuadráticas│compilado de problemas
• 282. Ecuaciones cuadráticas│problema 1
• 283. Ecuaciones cuadráticas│problema 2
• 284. Ecuaciones cuadráticas│problema 3
• 285. Ecuaciones cuadráticas│problema 4
• 286. Ecuaciones cuadráticas│problema 5
• 287. Ecuaciones cuadráticas│problema 6
• 288. Ecuaciones cuadráticas│problema 7
• 289. Ecuaciones cuadráticas con Pitágoras
• 290. Problema de una ecuación cuadrática│difícil 1
• 291. Problema de una ecuación cuadrática│difícil 2

XI. Radicación

• 292. Radicación de números enteros│compilado
• 293. Radicación de números enteros│ejercicio 1
• 294. Radicación de un número│exponente fraccionario
• 295. Radicación de expresiones algebraicas│compilado
• 296. Radicación de expresiones algebraicas│ejercicio 1
• 297. Radicación de expresiones algebraicas│ejercicio 2
• 298. Radicación de expresiones algebraicas │ejercicio 3
• 299. ✅ Como SUMAR y RESTAR radicales
• 300. Factorizar suma de raíces
• 301. Radicación de fracciones│compilado
• 302. Radicación de fracciones│ejercicio 1
• 303. Como RACIONALIZAR números FRACCIONARIOS
• 304. Como RACIONALIZAR un PRODUCTO de números
• 305. Como RACIONALIZAR la RAÍZ de una RAÍZ de números
• 306. Racionalización del denominador│monomio
• 307. Racionalización del denominador│binomio
• 308. Racionalización del denominador│ejercicio 1
• 309. Racionalización del denominador│ejercicio 2

XII. Ecuaciones con radicales

• 310. Ecuaciones con radicales │ejercicio 1
• 311. Ecuaciones con radicales│ejercicio 4
• 312. Ecuaciones con raíz cuadrada
• 313. Ecuaciones con raíz cuadrada│problema

XIII. Inecuaciones (desigualdades)

• 314. Introducción a las desigualdades
• 315. Operaciones que no satisfacen una desigualdad
• 316. Desigualdad con 3 variables
• 317. Desigualdad lineal con una constante│ej 1
• 318. Desigualdad lineal con gráfica│ej 1
• 319. Desigualdad lineal con una constante│ej 2
• 320. Desigualdad lineal con gráfica│ej 2
• 321. Desigualdad lineal racional│ejercicio 1
• 322. Desigualdad lineal racional│ejercicio 2
• 323. Desigualdad lineal con tres componentes│ej 1
• 324. Desigualdad lineal con tres componentes│ej 2
• 325. Desigualdad lineal con valor absoluto│ejercicio 1
• 326. Desigualdad lineal con fracciones│ejercicio 1
• 327. Desigualdad lineal con fracciones│ejercicio 2
• 328. Desigualdad cúbica
• 329. Inecuaciones cuadráticas │ ejercicio 1
• 330. Inecuaciones cuadráticas │ ejercicio 2

XIV. 5 errores típicos en álgebra

• 331. 5 errores comunes en álgebra

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