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 32+4(2+n)=16\frac{3}{2+4(2+n)}=\frac{1}{6}?

Here are the steps:



32+4(2+n)=16\frac{3}{2+4(2+n)}=\frac{1}{6}

1
Factor out the common term 22.
32(1+2(2+n))=16\frac{3}{2(1+2(2+n))}=\frac{1}{6}

2
Multiply both sides by 2(1+2(2+n))2(1+2(2+n)).
3=16×2(1+2(2+n))3=\frac{1}{6}\times 2(1+2(2+n))

3
Use this rule: ab×cd=acbd\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}.
3=1×2(1+2(2+n))63=\frac{1\times 2(1+2(2+n))}{6}

4
Simplify  1×2(1+2(2+n))1\times 2(1+2(2+n))  to  2(1+2(2+n))2(1+2(2+n)).
3=2(1+2(2+n))63=\frac{2(1+2(2+n))}{6}

5
Simplify  2(1+2(2+n))6\frac{2(1+2(2+n))}{6}  to  1+2(2+n)3\frac{1+2(2+n)}{3}.
3=1+2(2+n)33=\frac{1+2(2+n)}{3}

6
Multiply both sides by 33.
3×3=1+2(2+n)3\times 3=1+2(2+n)

7
Simplify  3×33\times 3  to  99.
9=1+2(2+n)9=1+2(2+n)

8
Subtract 11 from both sides.
9−1=2(2+n)9-1=2(2+n)

9
Simplify  9−19-1  to  88.
8=2(2+n)8=2(2+n)

10
Divide both sides by 22.
82=2+n\frac{8}{2}=2+n

11
Simplify  82\frac{8}{2}  to  44.
4=2+n4=2+n

12
Subtract 22 from both sides.
4−2=n4-2=n

13
Simplify  4−24-2  to  22.
2=n2=n

14
Switch sides.
n=2n=2

Done
Cymath foriOSAndroid