Question

Halla la solucion de cada ecuacion
a.x-6/4 - 2x+1/2 -3=x/3 -1/2
b.x-1/6 - 3x+2/3 +1 = ×/12 + 1/6

Answer 1

Halla la solución de cada ecuación

a. x-6/4 - 2x+1/2 -3=x/3 -1/2

$\mathrm{Agrupar\:terminos\:semejantes}\\\\x-2x-3-\frac{6}{4}+\frac{1}{2}=\frac{x}{3}-\frac{1}{2}\\\\\mathrm{Sumar\:elementos\:similares:}\:x-2x=-x\\\\-x-3-\frac{6}{4}+\frac{1}{2}=\frac{x}{3}-\frac{1}{2}\\\\-x-3-\frac{3}{2}+\frac{1}{2}=\frac{x}{3}-\frac{1}{2}\\\\-x-3-1=\frac{x}{3}-\frac{1}{2}\\\\-x-4=\frac{x}{3}-\frac{1}{2}\\\\-x-4+4=\frac{x}{3}-\frac{1}{2}+4\\\\-x=\frac{7}{2}+\frac{x}{3}\\\\-x-\frac{x}{3}=\frac{7}{2}+\frac{x}{3}-\frac{x}{3}\\\\-\frac{4x}{3}=\frac{7}{2}$

$\mathrm{Multiplicar\:ambos\:lados\:por\:}3\\\\3\left(-\frac{4x}{3}\right)=\frac{7\cdot \:3}{2}\\\\-4x=\frac{21}{2}\\\\\frac{-4x}{-4}=\frac{\frac{21}{2}}{-4}\\\\x=-\frac{21}{8}$

b.x-1/6 - 3x+2/3 +1 = ×/12 + 1/6

$\mathrm{Agrupar\:terminos\:semejantes}\\\\-3x+1-\frac{1}{6}+\frac{2}{3}=\frac{x}{12}+\frac{1}{6}\\\\\mathrm{Sumar\:elementos\:similares:}\:x-3x=-2x\\\\-2x+1-\frac{1}{6}+\frac{2}{3}=\frac{x}{12}+\frac{1}{6}\\\\\mathrm{Convertir\:a\:fraccion}:\quad \:1=\frac{1}{1}\\\\\frac{1}{1}-\frac{1}{6}+\frac{2}{3}=\frac{x}{12}+\frac{1}{6}\\\\\mathrm{Reescribir\:las\:fracciones\:basandose\:en\:el\:minimo\:comun\:denominador}\\\\\frac{6}{6}-\frac{1}{6}+\frac{4}{6}=\frac{x}{12}+\frac{1}{6}$

$\mathrm{Ya\:que\:los\:denominadores\:son\:iguales,\:combinar\:las\:fracciones}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\\frac{6-1+4}{6}=\frac{x}{12}+\frac{1}{6}\\\\\mathrm{Sumar/restar\:lo\:siguiente:}\:6-1+4=9\\\\\frac{9}{6}=\frac{x}{12}+\frac{1}{6}\\\\\mathrm{Eliminar\:los\:terminos\:comunes:}\:3\\\\-2x+\frac{3}{2}=\frac{x}{12}+\frac{1}{6}\\\\\mathrm{Restar\:}\frac{3}{2}\mathrm{\:de\:ambos\:lados}\\\\-2x+\frac{3}{2}-\frac{3}{2}=\frac{x}{12}+\frac{1}{6}-\frac{3}{2}$

$-\frac{25x}{12}=-\frac{4}{3}\\\\\mathrm{Multiplicar\:ambos\:lados\:por\:}12\\\\12\left(-\frac{25x}{12}\right)=12\left(-\frac{4}{3}\right)\\\\-25x=-16\\\\x=\frac{16}{25}$