Problem of the Week

Updated at Apr 22, 2019 5:15 PM

This week's problem comes from the equation category.

How can we solve the equation \(\frac{4m}{5(2+{m}^{2})}=\frac{4}{15}\)?

Let's begin!



\[\frac{4m}{5(2+{m}^{2})}=\frac{4}{15}\]

1
Multiply both sides by \(5(2+{m}^{2})\).
\[4m=\frac{4}{15}\times 5(2+{m}^{2})\]

2
Simplify \(\frac{4}{15}\times 5(2+{m}^{2})\) to \(\frac{4(2+{m}^{2})}{3}\).
\[4m=\frac{4(2+{m}^{2})}{3}\]

3
Multiply both sides by \(3\).
\[12m=4(2+{m}^{2})\]

4
Divide both sides by \(4\).
\[3m=2+{m}^{2}\]

5
Move all terms to one side.
\[3m-2-{m}^{2}=0\]

6
Multiply both sides by \(-1\).
\[{m}^{2}-3m+2=0\]

7
How?
Factor \({m}^{2}-3m+2\).
\[(m-2)(m-1)=0\]

8
How?
Solve for \(m\).
\[m=2,1\]

Done