Problem of the Week

Updated at Jan 18, 2021 9:03 AM

This week we have another equation problem:

How can we solve the equation \(4+4\times \frac{5}{2+n}=\frac{22}{3}\)?

Let's start!



\[4+4\times \frac{5}{2+n}=\frac{22}{3}\]

1
Simplify  \(4\times \frac{5}{2+n}\)  to  \(\frac{20}{2+n}\).
\[4+\frac{20}{2+n}=\frac{22}{3}\]

2
Subtract \(4\) from both sides.
\[\frac{20}{2+n}=\frac{22}{3}-4\]

3
Simplify  \(\frac{22}{3}-4\)  to  \(\frac{10}{3}\).
\[\frac{20}{2+n}=\frac{10}{3}\]

4
Multiply both sides by \(2+n\).
\[20=\frac{10}{3}(2+n)\]

5
Simplify  \(\frac{10}{3}(2+n)\)  to  \(\frac{10(2+n)}{3}\).
\[20=\frac{10(2+n)}{3}\]

6
Multiply both sides by \(3\).
\[20\times 3=10(2+n)\]

7
Simplify  \(20\times 3\)  to  \(60\).
\[60=10(2+n)\]

8
Divide both sides by \(10\).
\[\frac{60}{10}=2+n\]

9
Simplify  \(\frac{60}{10}\)  to  \(6\).
\[6=2+n\]

10
Subtract \(2\) from both sides.
\[6-2=n\]

11
Simplify  \(6-2\)  to  \(4\).
\[4=n\]

12
Switch sides.
\[n=4\]

Done
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