Question

Resolver las siguientes ecuaciones con fracciones
5x+7/2-x+4/5=1-(3-x/4)

Answer 1

Respuesta:

X=-42/25=-1.68

Explicación paso a paso:

Aislarlo en un lado de la ecuación para obtener la respuesta final.

Combina los términos semejantes (grupo de términos semejantes).

$\displaystyle \mathsf{5x-x+\frac{7}{2}+\frac{4}{5}=1-\left(3-\frac{x}{4}\right)}}\\\\\\\displaystyle \mathsf{5x-x=4x}}\\\\\\\displaystyle \mathsf{4x+\frac{7}{2}+\frac{4}{5}=1-\left(3-\frac{x}{4}\right)}}\\\\\\\textbf{minimo comun multiplo (LCM):}\\\\\\\displaystyle \mathsf{2,5=10}}\\\\\\\displaystyle \mathsf{\frac{35}{10}+\frac{8}{10}=1-\left(3-\frac{x}{4}\right)}}\\\\\\\displaystyle \mathsf{\frac{35+8}{10}=1-\left(3-\frac{x}{4}\right)}}\\\\\\\textbf{Anadir.}$

$\displaystyle \mathsf{35+8=43}}\\\\\\\displaystyle \mathsf{4x+\frac{43}{10}=1-\left(3-\frac{x}{4}\right)}\\\\\\\textbf{Resta por 43/10 de ambos lados.}\\\\\\\displaystyle \mathsf{4x+\frac{43}{10}-\frac{43}{10}=1-\left(3-\frac{x}{4}\right)-\frac{43}{10}}\\\\\\\textbf{Resolver.}\\\\\displaystyle \mathsf{4x=-\frac{63}{10}+\frac{x}{4}}}\\\\\textbf{Resta por x / 4 de ambos lados.}\\\\\\\displaystyle \mathsf{4x-\frac{x}{4}=-\frac{63}{10}+\frac{x}{4}-\frac{x}{4}}}\\\\\\\textbf{Resolver.}$

$\displaystyle \mathsf{\frac{15x}{4}=-\frac{63}{10}}}}\\\\\\\textbf{Multiplicar por 4 desde ambos lados.}}\\\\\\\displaystyle \mathsf{\frac{4\cdot \:15x}{4}=4\left(-\frac{63}{10}\right)}}\\\\\\\textbf{Resolver.}}\\\\\\\displaystyle \mathsf{15x=-\frac{126}{5}}}\\\\\\\textbf{Dividir por 15 desde ambos lados.}}\\\\\\\dislaystyle \mathsf{\frac{15x}{15}=\frac{-\frac{126}{5}}{15}}}\\\\\\\textbf{Resolver.}\\\\\displaystyle \mathsf{x=-\frac{42}{25} }}$

$\longrightarrow \Large\boxed{\mathsf{x=-\frac{42}{25}=-1.68 }}$