Question

hallar el valor de la x​

Answer 1

$\bold{RESOLVIENDO:}$

$\text{a)}\cdot \text{Planteamos la ecuaci\'on de primer grado, y lo resolvemos por igualaci\'on.}$

$\dfrac{x-1}{3} = \dfrac{4-6x}{10}-1$

$\dfrac{x-1}{3} = \dfrac{4-6x-10}{10}\quad\to\text{Utilizamos la multiplicaci\'on cruzada. }$

$10\left(x-1\right) = 3\left(4-6x-10\right)\quad\to\text{Multiplicas en asma. }$

$10x -10 = 12-18x-30\quad\to\text{Desarrollamos.}$

$10x -10 = -18-18x$

$10x + 18x= -18+10$

$28x= -8$

$x=\dfrac{-8}{28}$

$x=-\dfrac{2}{7}\quad\Longrightarrow\boxed{\bold{RESULTADO.}}$

$\bold{COMPROBACI\'ON:}\\\\\dfrac{\left(-\dfrac{2}{7}\right) -1}{3} = \dfrac{4-6\left(-\dfrac{2}{7}\right) }{10} -1\\\\ \dfrac{-\dfrac{2}{7}-1}{3}= \dfrac{4+6\cdot \dfrac{2}{7}}{10} -1\\\\\dfrac{\dfrac{-2-7}{7}}{3}= \dfrac{4+\dfrac{12}{7}}{10} -1\\\\\dfrac{\dfrac{-9}{7}}{3}= \dfrac{\dfrac{40}{7}}{10} -1\\\\\dfrac{-9}{7\cdot 3}= \dfrac{40}{70} -1\\\\\dfrac{-9}{21}= \dfrac{4-7}{7} \\\\-\dfrac{3}{7} = -\dfrac{3}{7}$

$\bold{RESOLVIENDO:}$

$\text{b)}\cdot \text{Planteamos la ecuaci\'on de primer grado, y lo resolvemos por igualaci\'on.}$

$\dfrac{3}{4}x-1= 1.5x+\dfrac{2x-1}{3} -2.5$

$\dfrac{3}{4}x\cdot 10-1\cdot10= 1.5x\cdot 10+\dfrac{2x-1}{3} \cdot 10 -2.5\cdot 10\to\text{Multiplicar por 10.}$

$\dfrac{15}{2}x-10= 15x+\dfrac{10\left(2x-1\right)}{3} -25$

$\dfrac{15}{2}x= 15x+\dfrac{10\left(2x-1\right)}{3} -25+10$

$\dfrac{15}{2}x=\dfrac{65x-10}{3} -15$

$\dfrac{15}{2}x\cdot 6= \dfrac{6\left(65x-10\right)}{3} -15\cdot6$

$45x= 2\left(65x-10\right) -90$

$45x= 130x-20 -90$

$45x= 130x-110$

$45x- 130x= -110$

$-85x= -110$

$x=\dfrac{-110}{-85}$

$x=\dfrac{22}{17}\quad\Longrightarrow\boxed{\bold{RESULTADO.}}$