Assignment [MatS-7/N-XX1-K05]

Einsendeaufgabe ILS - Lineare Gleichungen: MatS 7N - Mathematik

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Mathematics
MatS-7/N-XX1-K05

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ILS Institut für Lernsysteme - Fernhochschule Hamburg

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1,00, G. Kühnberger, 2017

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Einsendeaufgabe MatS 7/N-XX1-K05 22.03.2017 Aufgabe 1 a) 2x – 4 = 4x – 5 = 2x – 4 = 4x – 5 | + 5 = 2x + 1 = 4x | - 2x = 1 = 2x | : 2 = 0,5 = x b) 3x + 4x – 7 = 12 + x = 3x + 4x – 7 = 12 + x | - 12 = 7x – 19 = x | - 7x ..…

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Einsendeaufgabe ILS - Lineare Gleichungen: MatS 7N - Mathematik


Aufgabe 1


a)                    2x - 4 = 4x - 5                                                | -2x   +5

            Û        1 = 2x                                                             | : 2

            Û        x = 0,5


b)                    3x + 4x - 7 = 12 + x

            Û        7x - 7 = 12 + x                                               | -x   +7

            Û        6x = 19                                                           | : 6

            Û        x  3,16


c)                    x -  = 0,8                                               | +


            Û        x = 1                                                          | :


            Û                x = 3

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⊇)                    2(≠-3) + 2(3≠ + 4) = 10

            Û        2≠ - 6 + 6≠ + 8 = 10

            Û        8≠ + 2 = 10                                                    | -2

            Û        8≠ = 8                                                             | : 8

            Û        ≠ = 1


∞)                    5(≠ - 3) = 2(≠ + 1) - 5(≠ - 3)

            Û        5≠ - 15 = 2≠ + 2 - 5≠ + 15

            Û        5≠ - 15 = -3≠ + 17                                          | +3≠

            Û        8≠ - 15 = 17                                                   | +15

            Û        8≠ = 32                                                           | : 8

            Û        ≠ = 4


†)                     (≠ - 2)² - (≠ - 1)² = -2≠ + 1

            Û        (≠² - 4≠ + 4) - (≠² - 2≠ + 1) = -2≠ + 1

            Û        ≠² - 4≠ + 4 - ≠² + 2≠ - 1 = -2≠ + 1

            Û        -2≠ + 3 = -2≠ + 1                                           | + 2≠

            Û        3 1        †++ ⊇;∞≈∞ 6†∞;≤+∞≈⊥ ⊥;+† ∞≈ ∂∞;≈∞ 7+≈∞≈⊥


4∞†⊥∋+∞ 2


                        (≠ + 7)3 - 6 = 2≠

            Û        3≠ + 21 - 6 = 2≠

            Û        3≠ + 15 = 2≠                                                  | -15

            Û        3≠ = 2≠ - 15                                                   | - 2≠

            Û        ≠ = -15


8;∞ ⊥∞≈∞≤+†∞ 5∋+† †∋∞†∞† -15


.....


≠ = 6∋++=∞;† =+≈ 9∋+† ∞≈⊇ 0††+ ;≈ 3†∞≈⊇∞≈


9∋+† †∞⊥† +;≈ =∞∋ 7+∞††∞≈ 12≠ ∂∋ =∞++≤∂

0††+ †∞⊥† +;≈ =∞∋ 7+∞††∞≈ 10(≠ - 0,5) ∂∋ =∞++≤∂

8;∞ ⊥∞∋∞;≈≈∋∋ =∞ +∞≠=††;⊥∞≈⊇∞ 3†+∞≤∂∞ +∞†+=⊥† 39 ∂∋


                        12≠ + 10(≠ - 0,5) = 39

            Û        12≠ + 10≠ - 5 = 39

            Û        22≠ - 5 = 39                                                    | +5

            Û        22≠ = 44                                                         | : 22

            Û        ≠ = 2


9∋+† ∞≈⊇ 0††+ †+∞††∞≈ ≈;≤+ =≠∞; 3†∞≈⊇∞≈, ≈∋≤+⊇∞∋ 9∋+†

∋∞†⊥∞+++≤+∞≈ ;≈† - ∋†≈+ ∞∋ 17 0++


Um zu errechnen wie weit Karl gefahren ist rechnet man:


12 km/h in 2 Stunden = 24 km


Karl hat dabei eine Strecke von 24 km zurückgelegt, daher liegt der Treffpunkt von Karl und Otto 24 km von Karls Startpunkt entfernt.

 

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5∞+ 0+++∞ ∞++∞≤+≈∞† ∋∋≈ ⊇;∞ 3†+∞≤∂∞, ⊇;∞ 0††+ =∞++≤∂⊥∞†∞⊥† +∋†


10 ∂∋/+ ;≈ (2 - 0,5) ∋†≈+ 1,5 3†∞≈⊇∞≈  = 15 ∂∋


∞≈⊇ ∋⊇⊇;∞+† ⊇;∞ 3†+∞≤∂∞≈ =+≈ 9∋+† ∞≈⊇ 0††+. 3∞≈≈ ⊇;∞ 5∞≤+≈∞≈⊥ +;≤+†;⊥ ;≈†, ∋∞≈≈ ≈;≤+ ⊇;∞ 6∞≈∋∋†≈†+∞≤∂† =+≈ 39∂∋ ∞+⊥∞+∞≈.


0+++∞: 24 + 15 = 39


4∞†⊥∋+∞ 4


∋)        8 = ℚ / {1; -1,5}


                        =                             | · (≠ - 1)


            Û        ≠ + 1 =                               | · (2≠ + 3)


            Û        (≠ + 1)(2≠ + 3) = (2≠ + 1)(≠ - 1)

            Û        2≠² + 3≠ + 2≠ + 3 = 2≠² - 2≠ + ≠ - 1

            Û        2≠² + 5≠ + 3 = 2≠² - ≠ - 1                               | - 2≠²

            Û        5≠ + 3 = -≠ - 1                                                | + ≠

            Û        6≠ + 3 = -1                                                     | - 3

            Û        6≠ = - 4                                                           | : 6

            Û        ≠ =                                                       | 9++=∞≈


            Û        ≠ =

                        ___


            0+++∞:

           

                        =


            Û        =


            Û        - =  -

                        ______


+)        8 =  ℚ / {-1; -2}


                         - = 1                        | · (≠ + 1)


            Û        3≠ - = 1 (≠ + 1).....


            Û        3≠ (≠ + 2) - 2≠ (≠ + 1) = 1 (≠ + 1)(≠ + 2)

            Û        3≠² + 6≠ - 2≠² - 2≠ = 1(≠² + 2≠ + 1≠ + 2)

            Û        ≠² + 4≠ = ≠² + 3≠ + 2                                      | -≠²

            Û        4≠ = 3≠ + 2                                                     | - 3≠

            Û        ≠ = 2

           

            0+++∞:

           

                        - = 1


            Û        - = 1


            Û        2 - 1 = 1


            Û        1 = 1


5∞≈∋†=∋∞†⊥∋+∞


8 =  ℚ / {}


            + = +1                             | 9+≠∞;†∞+≈


Û        +  = +1


Û        +=+1        | -


Û           = 1            | · (15≠+ 5)


Û        17≠ - 5 + 32,5≠ - 2,5 - 35≠ + 15 = 15≠ + 5

Û        14,5≠ + 7,5 = 15≠ + 5                                                      | - 14,5≠

Û        7,5 = 0,5≠ + 5                                                                   | - 5

Û        2,5 = 0,5≠                                                                         | : 0,5

Û        ≠ = 5

0+++∞:


            + = + 1


Û        + = + 1


Û        1 + 2 = 2 + 1


Û        3 .....


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