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.
\[n=2\]

Done
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