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Hallar el valor de [tex]\(x\)[/tex]:

[tex]\[ 4(x-6) - 3x = 3x - (2 + 3(4 + 2x)) \][/tex]

(A) [tex]\(\frac{7}{9}\)[/tex]

(B) [tex]\(\frac{3}{4}\)[/tex]

(C) [tex]\(\frac{6}{7}\)[/tex]

(D) [tex]\(\frac{4}{5}\)[/tex]

(E) [tex]\(\frac{5}{2}\)[/tex]

Sagot :

GinnyAnsweridn
Claro, vamos a resolver la ecuación [tex]\( 4(x - 6) - 3x = 3x - (2 + 3(4 + 2x)) \)[/tex] paso a paso.

1. Expandir y simplificar ambos lados de la ecuación:

Para el lado izquierdo:
[tex]\[ 4(x - 6) - 3x = 4x - 24 - 3x = x - 24 \][/tex]

Para el lado derecho:
[tex]\[ 3x - (2 + 3(4 + 2x)) \][/tex]
Primero expandimos la expresión dentro del paréntesis:
[tex]\[ 2 + 3(4 + 2x) = 2 + 12 + 6x = 14 + 6x \][/tex]
Entonces:
[tex]\[ 3x - (14 + 6x) = 3x - 14 - 6x = -3x - 14 \][/tex]

2. Reescribir la ecuación con las expresiones simplificadas:
[tex]\[ x - 24 = -3x - 14 \][/tex]

3. Combinar términos semejantes para resolver para "x":

Sumamos [tex]\(3x\)[/tex] a ambos lados de la ecuación:
[tex]\[ x + 3x - 24 = -3x + 3x - 14 \][/tex]
Esto simplifica a:
[tex]\[ 4x - 24 = -14 \][/tex]
Sumamos 24 a ambos lados:
[tex]\[ 4x - 24 + 24 = -14 + 24 \][/tex]
Lo que simplifica a:
[tex]\[ 4x = 10 \][/tex]

4. Finalmente, resolver para "x" dividiendo ambos lados entre 4:
[tex]\[ x = \frac{10}{4} = \frac{5}{2} = 2.5 \][/tex]

El valor de [tex]\( x \)[/tex] es [tex]\( \frac{5}{2} \)[/tex]. Por lo tanto, la respuesta correcta es:
[tex]\( \boxed{5/2} = (E) \)[/tex].
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