Question

1/4x+1/6x=x-8..........no spam ​

Answer 1

Answer:

$\dfrac{1}{4}x+\dfrac{1}{6}x=x-8\quad :\quad x=\dfrac{96}{7}\quad \left(\mathrm{Decimal}:\quad x=13.71429\dots \right)$

Step-by-step explanation:

$\dfrac{1}{4}x+\dfrac{1}{6}x=x-8$

$\mathrm{Subtract\:}x\mathrm{\:from\:both\:sides}$

$\dfrac{1}{4}x+\dfrac{1}{6}x-x=x-8-x$

$\mathrm{Simplify}$

$\dfrac{1}{4}x+\dfrac{1}{6}x-x=x-8-x$

$\mathrm{Simplify\:}\dfrac{1}{4}x+\dfrac{1}{6}x-x$

$\mathrm{Factor\:out\:common\:term\:}x$

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

$\dfrac{1}{4}+\dfrac{1}{6}-1=-\dfrac{7}{12}$

$=-\dfrac{7}{12}x$

$\mathrm{Simplify\:}x-8-x:\quad -8$

$-\dfrac{7}{12}x=-8$

$\mathrm{Multiply\:both\:sides\:by\:}-12$

$\left(-\dfrac{7}{12}x\right)\left(-12\right)=\left(-8\right)\left(-12\right)$

$\mathrm{Simplify}$

$7x=96$

$\mathrm{Divide\:both\:sides\:by\:}7$

$\dfrac{7x}{7}=\dfrac{96}{7}$

$\mathrm{Simplify}$

$x=\dfrac{96}{7}$