Question

\frac{x-2}{2}-\frac{x+y}{14}=\frac{x-y-1}{8}-\frac{y+12}{4}

Answer 1

Answer:

$\mathrm{solve\:for\:x,\:\frac{x-2}{2}-\frac{x+y}{14}=\frac{x-y-1}{8}-\frac{y+12}{4}\quad :\quad x=-y-7}$

Step-by-step explanation:

$\mathrm{\frac{x-2}{2}-\frac{x+y}{14}=\frac{x-y-1}{8}-\frac{y+12}{4}}$

$\mathrm{Multiply\:by\:LCM=}56$

$\mathrm{\frac{x-2}{2}\cdot \:56-\frac{x+y}{14}\cdot \:56=\frac{x-y-1}{8}\cdot \:56-\frac{y+12}{4}\cdot \:56}$

$\mathrm{28\left(x-2\right)-4\left(x+y\right)=7\left(x-y-1\right)-14\left(y+12\right)}$

$\mathrm{24x-4y-56=7x-21y-175}$

$\mathrm{Add\:4y\mathrm{\:to\:both\:sides}}$

$\mathrm{24x-4y-56+4y=7x-21y-175+4y}$

$\mathrm{24x-56=-17y+7x-175}$

$\mathrm{Add\:}56\mathrm{\:to\:both\:sides}$

$\mathrm{24x-56+56=-17y+7x-175+56}$

$\mathrm{24x=7x-17y-119}$

$\mathrm{Subtract\:7x}\mathrm{\:from\:both\:sides}}$

$\mathrm{24x-7x=7x-17y-119-7x}$

$\mathrm{17x=-17y-119}$

$\mathrm{Divide\:both\:sides\:by\:}17$

$\mathrm{\frac{17x}{17}=-\frac{17y}{17}-\frac{119}{17}}$

$\mathrm{x=-y-7}$