# Problem of the Week

## Updated at Sep 4, 2023 3:31 PM

For this week we've brought you this equation problem.

How would you solve the equation $$\frac{3}{2+4(2+n)}=\frac{1}{6}$$?

Here are the steps:

$\frac{3}{2+4(2+n)}=\frac{1}{6}$

 1 Factor out the common term $$2$$.$\frac{3}{2(1+2(2+n))}=\frac{1}{6}$2 Multiply both sides by $$2(1+2(2+n))$$.$3=\frac{1}{6}\times 2(1+2(2+n))$3 Use this rule: $$\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}$$.$3=\frac{1\times 2(1+2(2+n))}{6}$4 Simplify  $$1\times 2(1+2(2+n))$$  to  $$2(1+2(2+n))$$.$3=\frac{2(1+2(2+n))}{6}$5 Simplify  $$\frac{2(1+2(2+n))}{6}$$  to  $$\frac{1+2(2+n)}{3}$$.$3=\frac{1+2(2+n)}{3}$6 Multiply both sides by $$3$$.$3\times 3=1+2(2+n)$7 Simplify  $$3\times 3$$  to  $$9$$.$9=1+2(2+n)$8 Subtract $$1$$ from both sides.$9-1=2(2+n)$9 Simplify  $$9-1$$  to  $$8$$.$8=2(2+n)$10 Divide both sides by $$2$$.$\frac{8}{2}=2+n$11 Simplify  $$\frac{8}{2}$$  to  $$4$$.$4=2+n$12 Subtract $$2$$ from both sides.$4-2=n$13 Simplify  $$4-2$$  to  $$2$$.$2=n$14 Switch sides.$n=2$Donen=2