Question

hallar el valor de x
$(2x - 4) \div 10 + 3 \div 4 = (6 + x) \div 5 \div 0.5$
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Answer 1

Hola'

hallar el valor de x:

$\dfrac{\left(2x-4\right)}{10}+\dfrac{3}{4}=\dfrac{\dfrac{\left(6+x\right)}{5}}{\dfrac{0,5}{}}$

Solución:

• paso 1: convertir 0,5 en fracción

• paso 2: resolver.

el paso 1:

$\dfrac{0,5 \cdot 10}{10}$

$= \dfrac{5}{10}$

→ simplificamos:

$=\dfrac{1}{2}$

$------$

paso 2:

reemplazo la fracción en nuestra ecuación:

$\dfrac{\left(2x-4\right)}{10}+\dfrac{3}{4}=\dfrac{\dfrac{\left(6+x\right)}{5}}{\dfrac{1}{2 }}$

RESOLVIENDO:

$\dfrac{\left(2x-4\right)}{10}+\dfrac{3}{4}=\dfrac{\dfrac{\left(6+x\right)}{5}}{\dfrac{1}{2 }}$

→ quito los parentesis:

$\dfrac{\left2x-4\right}{10}+\dfrac{3}{4}=\dfrac{\dfrac{\left6+x\right}{5}}{\dfrac{1}{2 }}$

→ desarrollar:

$\dfrac{x}{5} - \dfrac{2}{5} +\dfrac{3}{4} = \dfrac{12}{5} + \dfrac{2x}{5}$

→ multiplicar ambos lados por 5:

$\dfrac{x}{5} \cdot 5- \dfrac{2}{5}\cdot5 +\dfrac{3}{4} \cdot5= \dfrac{12}{5}\cdot5 + \dfrac{2x}{5}\cdot5$

→ simplificar:

$x - 2+\dfrac{15}{4} = 12+2x$

→ desarrollar: x - 2 + 15/ 4:  x + 7/4

$x + \dfrac{7}{4} = 12 + 2x$

→ restar 7/4 ambos lados:

$x + \dfrac{7}{4} - \dfrac{7}{4} = 12 + 2x - \dfrac{7}{4}$

→ simplificar:

$x = 2x + \dfrac{41}{4}$

→ resta 2x ambos lados:

$x - 2x= 2x + \dfrac{41}{4} - 2x$

→ simplificamos:  

$-x = \dfrac{41}{4}$

→ dividir ambos lados entre -1:

$\dfrac{-x}{-1}=\dfrac{\dfrac{\left41\right}{4}}{\dfrac{-1}{}}$

→ y simplificamos:

$\boxed{x =- \dfrac{41}{4} }$

y listo la respuesta de x es = -(41 / 4):

COMPROBAMOS:

$\dfrac{\left(2x-4\right)}{10}+\dfrac{3}{4}=\dfrac{\dfrac{\left(6+x\right)}{5}}{\dfrac{1}{2 }}$

$\dfrac{\left(2\cdot(-\dfrac{41}{4}) -4\right)}{10}+\dfrac{3}{4}=\dfrac{\dfrac{\left(6+(-\dfrac{41}{4}) \right)}{5}}{\dfrac{1}{2 }}$

$\dfrac{\left-2\cdot\dfrac{41}{4} -4\right}{10}+\dfrac{3}{4}=\dfrac{\dfrac{\left(6-\dfrac{41}{4} \right)}{5}}{\dfrac{1}{2 }}$

$-\dfrac{49}{20} + \dfrac{3}{4} = \dfrac{\left(6-\dfrac{41}{4}\right)\cdot 2 }{5\cdot1}$

$-\dfrac{49}{20}+\dfrac{15}{20} = \dfrac{2\left(- \dfrac{17}{4}\right) }{5}$

$\dfrac{-49+15}{20} = \dfrac{- \dfrac{17}{4}\cdot2 }{5}$

$\dfrac{-34}{20} = -\dfrac{ \dfrac{17}{2} }{5}$

$-\dfrac{34}{20} =- \dfrac{17}{2\cdot5}$

$\boxed{-\dfrac{17}{20} =- \dfrac{17}{20}}$