Como un amante de las Matemáticas, este es mi aporte para todos esos estudiantes que desean preparase mejor, practicando diversos ejercicios, ya que esta es una de las materias que a la mayoría de jóvenes se les hace más complicada.
En el Blog iré colgando todos los ejercicios que vaya resolviendo

sábado, 5 de diciembre de 2009

Resolución de ecuaciones de primer grado con signos de agrupación

Ejercicios Resueltos de Algebra (A. Baldor)


Resolución de ecuaciones de primer grado con signos de agrupación

Ejercicios 79



1.-       X – (2X + 1) = 8 – (3X + 3)

             X – 2X – 1 = 8 – 3X – 3

              X – 2X + 3X = 8 – 3 + 1

                4X – 2X = 9 – 3

                  2X = 6

                  X = 6 / 2

                   X = 3         Respuesta


2.-        15X – 10 = 6X – (X + 2) + (–X + 3)

              15X – 10 = 6X – X – 2 – X + 3

               15X – 6x + X + X = – 2 + 3 + 10

                   11X = 11

                    X = 11 / 11

                      X = 1       Respuesta


3.-                (5 – 3X) – (– 4X + 6) = (8X + 11) – (3X – 6)

                       5 – 3X + 4X – 6 = 8X + 11 – 3X + 6

                         – 3X + 4X – 8X + 3X = 11 + 6 – 5 + 6

                             – 11X + 7X = 23 – 5

                                   – 4X = 18

                                     X = – 18 / 4

                                    X = – 9 / 2            Respuesta


4.-               30X – (–X + 6) + (– 5X + 4) = – (5X + 6) + (– 8 + 3X)

                    30X + X – 6 – 5X + 4 = – 5X – 6 – 8 + 3X

                     30X + X – 5X + 5X – 3X = – 6 – 8 + 6 – 4

                         36X – 8X = – 18 + 6

                             28X = – 12

                              X = – 12 / 28

                            X = – 3 / 7          Respuesta


5.-               15X + (–6X + 5) – 2 – (– X + 3) = – (7X + 23) – X + (3 + 2X)

                       15X – 6X + 5 – 2 + X – 3 = – 7X – 23 – X + 3 + 2X

                         16X – 6X +5 – 5 = – 8X – 23 + 3 + 2X

                             10X = – 20 – 10X

                              10X + 10X = – 20

                                   20X = – 20

                                 X = – 20 / 20

                                    X = – 1              Respuesta


6.-                3X + ( – 5X – (X + 3) ) = 8X + (–5X – 9)

                      3X + ( – 5X – X – 3) = 8X –5X – 9

                               3X + ( – 6X – 3 ) = 3X – 9

                                  – 3X – 3 = 3X – 9

                                        – 6X = – 6

                                          X = – 6 / – 6

                                            X = 1            Respuesta


7.-             16X – 3x – (6 – 9x) ) = 30X + ( – (3X + 2) – (X + 3) ).

                    16X – ( 3X – 6 + 9x  ) = 30X +  – 3X – 2 – X – 3 )

                        16X – 3X + 6 – 9X = 30X – 3X – 2 – X – 3

                             16X – 12X + 6 = 30X – 4X – 5

                                    4X – 26X = – 5 – 6

                                 – 22X = – 11      Signos negativos se eliminan

                                        22X = 11

                                        X = 11/ 22

                                          X = 1 / 2           Respuesta



8.-                X – ( 5 + 3X – ( 5X – (6 + X) )  = – 3

                        X – ( 5 + 3X – (5X – 6 – X ) )    = – 3

                            X – 5 + 3X – 5X + 6 + X  ) =  – 3

                                   X – 5 – 3X + 5X – 6 – X = – 3

                                           2X – 11 = – 3

                                            2X = – 3 + 11

                                             2X = 8

                                             X = 8/ 2

                                               X = 4          Respuesta

9.-                  9X – (5X + 1) –  2 + 8X – (7X – 5)  ) + 9X = 0

                         9X – (5X + 1) –  ( 2 + 8X – 7X + 5  + 9X = 0

                            9X – 5X – 1 – 2 – 8X + 7X – 5 + 9X = 0

                                        25X – 13X – 8 = 0

                                         12X = 8

                                          X = 8 / 12

                                 X = 2 / 3         Respuesta


10.-        71 + ( – 5X + (– 2X + 3) ) = 25 – – (3X + 4) – (4X + 3) ) .

                  71 + ( – 5X – 2X + 3 ) = 25 –  ( – 3X – 4 – 4X – 3 ) .

                     71 – 5X – 2X + 3 = 25 + 3X + 4 + 4X + 3

                             74 – 7X = 32 + 7X

                               – 7X – 7X = 32 – 74

                               – 14X = – 42     Signos negativos se eliminan

                                     14X = 42

                                      X = 42 / 14

                                      X = 3         Respuesta


11-       –  ( 3X + 8 – ( – 15 + 6X – (– 3X + 2) – (5X + 4) ) – 29 ) = – 5

                 –  ( 3X + 8 – ( – 15 + 6X + 3X – 2 – 5X – 4  – 29 ) = – 5

                    –  ( 3X + 8 + 15 – 6X – 3X + 2 + 5X + 4 – 29 )  = – 5

                       – 3X – 8 – 15 + 6X + 3X – 2 –5X – 4 + 29 = – 5

                                – 8X – 29 + 9X + 29 = – 5

                                    X = 5         Respuesta

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