Question

|-2n+6|=6
I believe it is absolute value. Please help asp

Answer 1

`n=0\quad \mathrm{or}\quad \:n=6`

Explanation:

`\left|-2n+6\right|=6\\\mathrm{Apply\:absolute\:rule}:\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\-2n+6=-6\quad \mathrm{or}\quad \:-2n+6=6\\-2n+6=-6\quad :\quad n=6\\-2n+6=-6\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\-2n+6-6=-6-6\\\mathrm{Simplify}\\-2n=-12\\\mathrm{Divide\:both\:sides\:by\:}-2\\(-2n)/(-2)=(-12)/(-2)\\`

`Simplify\\(-2n)/(-2)=(-12)/(-2)\\\mathrm{Simplify\:}(-2n)/(-2):\quad n\\(-2n)/(-2)\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(-b)=(a)/(b)\\=(2n)/(2)\\\mathrm{Divide\:the\:numbers:}\:(2)/(2)=1\\=n`

`\mathrm{Simplify\:}(-12)/(-2):\quad 6\\(-12)/(-2)\\\mathrm{Apply\:the\:fraction\:rule}:\quad (-a)/(-b)=(a)/(b)\\=(12)/(2)\\\mathrm{Divide\:the\:numbers:}\:(12)/(2)=6\\=6\\n=6\\-2n+6=6\quad :\quad n=0\\-2n+6=6\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\-2n+6-6=6-6\\Simplify\\-2n=0\\\mathrm{Divide\:both\:sides\:by\:}-2\\(-2n)/(-2)=(0)/(-2)`

`Simplify\\n=0\\\mathrm{Combine\:Solutions:}\\n=0\quad \mathrm{or}\quad \:n=6`