Question

What is the solution set for the equation 2|-3n| + 10 = 50

I

Answer 1

`n=-(20)/(3)\quad \mathrm{or}\quad \:n=(20)/(3)`

Explanation:

`2\left|-3n\right|+10=50\\\\\mathrm{Subtract\:}10\mathrm{\:from\:both\:sides}\\\\2\left|-3n\right|+10-10=50-10\\\\Simplify\\\\2\left|-3n\right|=40\\\\\mathrm{Divide\:both\:sides\:by\:}2\\\\(2\left|-3n\right|)/(2)=(40)/(2)\\\\Simplify\\\\\left|-3n\right|=20\\\\\mathrm{Apply\:absolute\:rule}:\\\quad \mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\\`

`-3n=-20\quad \mathrm{or}\quad \:-3n=20\\\\-3n=-20\quad :\quad n=(20)/(3)\\\\-3n=20\quad :\quad n=-(20)/(3)\\\\n=-(20)/(3)\quad \mathrm{or}\quad \:n=(20)/(3)`