Problem of the Week

Updated at Jun 15, 2020 10:33 AM

This week we have another equation problem:

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

Let's start!



\[4(3-\frac{5}{3-n})=22\]

1
Divide both sides by \(4\).
\[3-\frac{5}{3-n}=\frac{22}{4}\]

2
Simplify  \(\frac{22}{4}\)  to  \(\frac{11}{2}\).
\[3-\frac{5}{3-n}=\frac{11}{2}\]

3
Subtract \(3\) from both sides.
\[-\frac{5}{3-n}=\frac{11}{2}-3\]

4
Simplify  \(\frac{11}{2}-3\)  to  \(\frac{5}{2}\).
\[-\frac{5}{3-n}=\frac{5}{2}\]

5
Multiply both sides by \(3-n\).
\[-5=\frac{5}{2}(3-n)\]

6
Simplify  \(\frac{5}{2}(3-n)\)  to  \(\frac{5(3-n)}{2}\).
\[-5=\frac{5(3-n)}{2}\]

7
Multiply both sides by \(2\).
\[-5\times 2=5(3-n)\]

8
Simplify  \(-5\times 2\)  to  \(-10\).
\[-10=5(3-n)\]

9
Divide both sides by \(5\).
\[-\frac{10}{5}=3-n\]

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

11
Subtract \(3\) from both sides.
\[-2-3=-n\]

12
Simplify  \(-2-3\)  to  \(-5\).
\[-5=-n\]

13
Multiply both sides by \(-1\).
\[5=n\]

14
Switch sides.
\[n=5\]

Done
Cymath foriOSAndroid