Question

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

I

Answer 1

Answer:

$n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}$

Step-by-step explanation:

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

$-3n=-20\quad \mathrm{or}\quad \:-3n=20\\\\-3n=-20\quad :\quad n=\frac{20}{3}\\\\-3n=20\quad :\quad n=-\frac{20}{3}\\\\n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}$

Answer 2

Answer:

$n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}$

Step-by-step explanation:

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

$-3n=-20\quad \mathrm{or}\quad \:-3n=20\\\\-3n=-20\quad :\quad n=\frac{20}{3}\\\\-3n=20\quad :\quad n=-\frac{20}{3}\\\\n=-\frac{20}{3}\quad \mathrm{or}\quad \:n=\frac{20}{3}$