Question

3.(x+6)=(2x+1).5-71 como lo resuelvo?????
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Answer 1

Utilizando la propiedad distributiva en ecuaciones de primer grado, obtenemos que x = 12. A continuacion, explicamos como obtenemos esto:

Recordando la propiedad distributiva:

      [tex]\boxed{\LARGE{\textit{a(b + c) = (a)(b) + (b)(c)}}}[/tex]

Utilizando ello resolvemos primero los parentesis y luego resolvemos normalmente lo demas:

      [tex]\large{\textsf{3(x + 6) = (2x + 1)(5) - 71}}\\\\\\\large{\textsf{3(x) + (3)(6) = (2x)(5) + (1)(5) - 71}}\\\\\\\large{\textsf{3x+ 18 = 10x + 5 - 71}}\\\\\\\large{\textsf{3x+ 18 = 10x - 66}}\\\\\\\large{\textsf{18 + 66 = 10x - 3x}}[/tex]

      [tex]\large{\textsf{84 = 7x}}\\\\\\\large{\textsf{84 : 7 = x}}\\\\\\\to \boxed{\boxed{\large{\boldsymbol{12 = x}}}}[/tex]

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Comprobacion:

Al sustituir x = 12 en la ecuacion debemos obtener la misma igualdad:

      [tex]\large{\textsf{3(12 + 6) = (2 * 12 + 1)(5) - 71}}\\\\\\\large{\textsf{3(18) = (24 + 1)(5) - 71}}\\\\\\\large{\textsf{54 = (25)(5) - 71}}\\\\\\\large{\textsf{54 = 125 - 71}}\\\\\\\to \boxed{\large{\boldsymbol{54 = 54}}}}[/tex]

Como obtenemos la misma igualdad, entonces comcluimos que x = 12 resuelve la ecuacion

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[tex]\boxed{\boxed{\huge{\textsc{Espero ter ajudado, boa sorte!!}}}}[/tex]