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Equacions de grau 1 amb parèntesi

Cal tenir en compte que un nombre davant d'un parèntesi multiplicant a tot el de dintre. Per eliminar el parèntesi aplicarem la que es coneix com a propietat distributiva.

begin mathsize 18px style bold italic a bold left parenthesis bold italic b bold plus bold italic c bold right parenthesis bold equals bold italic a bold times bold italic b bold plus bold italic a bold times bold italic c end style

 begin mathsize 18px style bold italic a bold left parenthesis bold italic b bold minus bold italic c bold right parenthesis bold equals bold italic a bold times bold italic b bold minus bold italic a bold times bold italic c end style     

I si hi ha un menys davant del parèntesi: 

begin mathsize 18px style bold minus bold left parenthesis bold italic b bold plus bold italic c bold right parenthesis bold equals bold minus bold italic b bold minus bold italic c end style

begin mathsize 18px style bold minus bold left parenthesis bold italic b bold minus bold italic c bold right parenthesis bold equals bold minus bold italic b bold minus bold left parenthesis bold minus bold italic c bold right parenthesis bold equals bold minus bold italic b bold plus bold italic c end style


Exemples:

  • 3 left parenthesis x minus 2 right parenthesis equals 3 x plus 3 left parenthesis negative 2 right parenthesis equals 3 x minus 6
  • negative 2 left parenthesis 3 x plus 5 right parenthesis equals negative 2 times 3 x plus left parenthesis negative 2 right parenthesis times 5 equals negative 6 x minus 10
  • 5 minus 2 left parenthesis x minus 3 right parenthesis equals 5 minus 2 times x minus 2 times left parenthesis negative 3 right parenthesis equals 5 minus 2 x plus 6


    • Exemple 1

         bold 3 bold left parenthesis bold italic x bold minus bold 5 bold right parenthesis bold plus bold 1 bold equals bold minus bold left parenthesis bold 4 bold minus bold italic x bold right parenthesis bold space 3 x minus 15 plus 1 equals negative 4 plus x space 3 x minus x equals negative 4 plus 15 minus 1 space space space space space space space 2 x equals 10 space space space space space space rightwards arrow space space x equals 10 over 2 space space space space rightwards arrow space space space space space box enclose x equals 5 end enclose space

    Exemple 2

          bold 5 bold minus bold 3 bold left parenthesis bold italic x bold minus bold 2 bold right parenthesis bold equals bold 1 bold minus bold left parenthesis bold 2 bold italic x bold plus bold 3 bold right parenthesis bold space bold space space 5 minus 3 x plus 6 equals 1 minus 2 x minus 3 space space space minus 3 x plus 2 x equals 1 minus 3 minus 5 minus 6 space space space space space space space space space space space space minus x equals negative 13 space space space space space space space space space space space space space space space box enclose space x equals 13 end enclose space

    Exemple 3

         bold minus bold 2 bold left parenthesis bold 3 bold italic x bold minus bold 1 bold right parenthesis bold minus bold 2 bold italic x bold equals bold 5 bold space bold space bold space bold space minus 6 x plus 2 minus 2 x equals 5 space space space space minus 6 x minus 2 x equals 5 minus 2 space space space space space space space space space space space minus 8 x equals 3 space space rightwards arrow space space x equals fraction numerator 3 over denominator negative 8 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space box enclose space x equals negative 3 over 8 end enclose space

       Observació: quan una fracció és negativa, el signe menys és preferible posar-lo al numerador o davant la fracció.

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