Hvordan løse likninger (flytte-bytte-regelen)

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Oppslagsverk>Algebra>Likninger og ulikheter>Likninger>Førstegradslikninger>Hvordan løse likninger (flytte-bytte-regelen)

Tidligere har du sett at likningen må være i balanse. Det betyr at dersom du gjør noe på den ene siden, må du gjøre det samme på den andre siden. Når du ønsker å addere eller subtrahere bort et ledd på den ene siden av likningen for å få $x$ alene, gjør du som følger:

Eksempel 1

Subtraherer på begge sider

\begin{array}{l} x + 3 & = 5 \\ x + 3 - 3 & = 5 - 3 \\ x + 0 & = 2 \\ x & = 2 \end{array}

Du ønsker å bli kvitt

3

på VS. Hvis du trekker fra

3

på VS, forsvinner

3

-tallet.

3

-tallet du trakk fra på VS må du også trekke fra på HS. Dermed har

3

-tallet dukket opp på den andre siden av likhetstegnet, men med motsatt fortegn!

Eksempel 2

Adderer på begge sider

\begin{array}{l} x - 4 & = 9 \\ x - 4 + 4 & = 9 + 4 \\ x + 0 & = 13 \\ x & = 13 \end{array}

Du ønsker å bli blitt

- 4

på VS. Hvis du legger til

4

på VS, forsvinner

4

-tallet.

4

-tallet du la til på VS, må du også legge til på HS. Dermed har

4

-tallet dukket opp på den andre siden av likhetstegnet, men med motsatt fortegn!

Det finnes en lettere metode enn å trekke fra eller legge til på begge sider. Denne metoden kaller vi flytte/bytte.

Regel

Flytte/bytte-metoden

1.: Flytt det leddet du vil bli kvitt, over på andre siden av likhetstegnet.
2.: Bytt fortegn på dette leddet.

Eksempel 3

Pluss flytte/bytte til minus

\begin{array}{l} x + 3 & = 5 \\ x & = 5 - 3 \\ x & = 2 \end{array}

+ 3

blir flyttet over på HS av likningen. Vi bytter fortegn slik at

+ 3

blir til

- 3

Eksempel 4

Minus flytte/bytte til pluss

\begin{array}{l} x - 4 & = 9 \\ x & = 9 + 4 \\ x & = 13 \end{array}

- 4

blir flyttet over på HS av likningen. Vi bytter fortegn slik at

- 4

blir til

+ 4

Hvorfor kan du flytte/bytte?

Hvorfor er det slik at du bare kan flytte/bytte? Tenk deg at skålvekten er i balanse. Når du flytter et ledd over i den andre skålen, skulle en tro at den andre skålen blir mye tyngre. Men siden du bytter fortegn samtidig, blir det som om du fjerner eller legger til leddet fra den andre skålen også!

Tenk på dette

Flytte/bytte-regelen er en forenkling av å utføre den samme handlingen på begge sider av likhetstegnet. Matematikken er fantastisk på den måten – nye regler du lærer, gjør livet ditt enklere!

Eksempel 5

Løs likningen $x + 13 = 20$
$\begin{array}{l} x + 13 & = 20 \\ x & = 20 - 13 \\ x & = 7 \end{array}$

Eksempel 6

Løs likningen $x - 41 = 69$

\begin{array}{l} x - 41 = 69 x & = 69 + 41 x & = 110Eksempel 7 Løs likningen 2 x + 3 = 7 + x \begin{array}{l} 2 x + 3 = 7 + x 2 x - x & = 7 - 3 x & = 4Eksempel 8 Løs likningen 5 x - 11 = - 3 + 4 x \begin{array}{l} 5 x - 11 = - 3 + 4 x 5 x - 4 x & = - 3 + 11 x & = 8Vil du vite mer? Registrer deg Det er gratis!Forrige oppslag Hva er en variabel? Vil du vite mer? Registrer deg Det er gratis! Neste oppslag Hvordan bli kvitt tallet foran xHvordan løse likninger (flytte-bytte-regelen) Tall og måling Algebra Grunnleggende algebra Likninger og ulikheter Likninger Førstegradslikninger Andregradslikninger Polynomdivisjon Likningssett Rasjonale likninger Irrasjonale likninger Potenslikninger Teknikker Ulikheter Logaritmer Geometri Statistikk og sannsynlighet Funksjoner BevisMeny Hjem Søk ChatOm oss Om House of Math Om ansatte Karriere Media Foredrag Blogg Kontakt support@houseofmath.com + 47 22 150 300 Bygdøy allé 23,
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Det betyr at dersom du gjør noe på den ene siden, må du gjøre det samme på den andre siden. Når du ønsker å addere eller subtrahere bort et ledd på den ene siden av likningen for å få                                                                                                                                                                                                                                          \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/math\u003e alene, gjør du som følger: \u003c/p\u003e      \u003cdiv class=\"tcolorbox fooexample\" id=\"tcolobox-477\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Eksempel 1\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"example-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSubtraherer\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003epå\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003ebegge\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003esider\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                              \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-label\"\u003e                                            \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                           \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-label\"\u003e                                            \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e0\u003c/mn\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-label\"\u003e                                            \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e Du ønsker å bli kvitt \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e på VS. Hvis du trekker fra \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e på VS, forsvinner \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e-tallet. \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e-tallet du trakk fra på VS må du også trekke fra på HS. Dermed har \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e-tallet dukket opp på den andre siden av likhetstegnet, men med motsatt fortegn!   \u003c/div\u003e  \u003c/div\u003e                                                                                                                                                                                                                         \u003cdiv class=\"tcolorbox fooexample\" id=\"tcolobox-478\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Eksempel 2\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"example-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eAdderer\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003epå\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003ebegge\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003esider\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                              \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e9\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-label\"\u003e                                            \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e9\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                           \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-label\"\u003e                                            \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e0\u003c/mn\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                               \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-label\"\u003e                                            \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                               \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                           \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e Du ønsker å bli blitt \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e på VS. Hvis du legger til \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e på VS, forsvinner \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e-tallet. \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e-tallet du la til på VS, må du også legge til på HS. Dermed har \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e-tallet dukket opp på den andre siden av likhetstegnet, men med motsatt fortegn!   \u003c/div\u003e  \u003c/div\u003e                                                                                                                                                                                                                    \u003cp class=\"indent\" \u003e     Det finnes en lettere metode enn å trekke fra eller legge til på begge sider. Denne metoden kaller vi \u003cspan  class=\"ec-lmri-12x-x-144\"\u003eflytte/bytte\u003c/span type=\"punct\"\u003e. \u003c/p\u003e      \u003cdiv class=\"tcolorbox foorule\" id=\"tcolobox-479\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Regel\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"rule-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eFlytte/bytte-metoden\u003c/span\u003e \u003c/h3\u003e      \u003c/p\u003e\u003cdl class=\"enumerate-enumitem\"\u003e\u003cdt class=\"enumerate-enumitem\"\u003e    1.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Flytt         det         leddet         du         vil         bli         kvitt,         over         på         andre         siden         av         likhetstegnet.         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     2.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Bytt         fortegn         på         dette         leddet.         \u003cp class=\"noindent\" \u003e\u003c/dd\u003e\u003c/dl\u003e \u003c/p\u003e   \u003c/div\u003e  \u003c/div\u003e                                                                                                                                                                                                                                  \u003cdiv class=\"tcolorbox fooexample\" id=\"tcolobox-480\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Eksempel 3\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"example-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003ePluss\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eflytte/bytte\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003etil\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eminus\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                               \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-label\"\u003e                                              \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                        \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                             \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-label\"\u003e                                              \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                        \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e blir flyttet over på HS av likningen. Vi bytter fortegn slik at \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e blir til \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/math type=\"punct\"\u003e.   \u003c/div\u003e  \u003c/div\u003e                                                                                                                                                                                                                         \u003cdiv class=\"tcolorbox fooexample\" id=\"tcolobox-481\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Eksempel 4\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"example-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eMinus\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eflytte/bytte\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003etil\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003epluss\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                               \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e9\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-label\"\u003e                                              \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                        \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e9\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                             \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-label\"\u003e                                              \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                        \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                 \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                             \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e blir flyttet over på HS av likningen. Vi bytter fortegn slik at \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e blir til \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math type=\"punct\"\u003e.   \u003c/div\u003e  \u003c/div\u003e                                                                                                                                                                                                                    \u003cp class=\"noindent\" \u003e \u003c/p\u003e \u003cp class=\"indent\" \u003e     \u003ch2 class=\"section-title\"\u003e \u003ca   id=\"x1-34000\"\u003e\u003c/a\u003eHvorfor kan du flytte/bytte?\u003c/h2\u003e \u003c/p\u003e\u003cp class=\"indent\" \u003e     Hvorfor er det slik at du bare kan flytte/bytte? Tenk deg at skålvekten er i balanse. Når du flytter et ledd over i den andre skålen, skulle en tro at den andre skålen blir mye tyngre. Men siden du bytter fortegn samtidig, blir det som om du fjerner eller legger til leddet fra den andre skålen også! \u003c/p\u003e                                                                                                                                                                                                                                               \u003cdiv class=\"tcolorbox foothink\" id=\"tcolobox-482\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Tenk på dette\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003eFlytte/bytte-regelen er en forenkling av å utføre den samme handlingen på begge sider av likhetstegnet. \u003c/p\u003e\u003cp class=\"noindent\" \u003eMatematikken er fantastisk på den måten – nye regler du lærer, gjør livet ditt enklere! \u003c/p\u003e  \u003c/div\u003e  \u003c/div\u003e                                                                                                                                                                                                                  \u003c/p\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-483\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Eksempel 5\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eLøs likningen \u003c/span\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                  \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                        \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-label\"\u003e                                  \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                 \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-label\"\u003e                                  \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e7\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                         \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e   \u003c/div\u003e  \u003c/div\u003e \u003cp class=\"noindent\" \u003e\u003c/b\u003e                                                                                                                                                                                                                                          \u003c/p\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-484\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Eksempel 6\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eLøs likningen \u003c/span\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e6\u003c/mn\u003e\u003cmn\u003e9\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                  \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e6\u003c/mn\u003e\u003cmn\u003e9\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                        \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-label\"\u003e                                  \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e6\u003c/mn\u003e\u003cmn\u003e9\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                 \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-label\"\u003e                                  \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                 \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e   \u003c/div\u003e  \u003c/div\u003e \u003cp class=\"noindent\" \u003e\u003c/b\u003e                                                                                                                                                                                                                                          \u003c/p\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-485\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Eksempel 7\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eLøs likningen \u003c/span\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e7\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                             \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e7\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                            \u003cmtd  class=\"align-label\"\u003e                             \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mtd\u003e                            \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e7\u003c/mn\u003e\u003cmstyle mathcolor=\"#E60000\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e 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