Problem of the Week

Updated at Feb 11, 2019 4:37 PM

How would you solve the equation \((4+4m)\times \frac{3-m}{5}=\frac{12}{5}\)?

Below is the solution.



\[(4+4m)\times \frac{3-m}{5}=\frac{12}{5}\]

1
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{(4+4m)(3-m)}{5}=\frac{12}{5}\]

2
Factor out the common term \(4\).
\[\frac{4(1+m)(3-m)}{5}=\frac{12}{5}\]

3
Multiply both sides by \(5\).
\[4(1+m)(3-m)=12\]

4
Expand.
\[12-4m+12m-4{m}^{2}=12\]

5
Simplify  \(12-4m+12m-4{m}^{2}\)  to  \(12+8m-4{m}^{2}\).
\[12+8m-4{m}^{2}=12\]

6
Cancel \(12\) on both sides.
\[8m-4{m}^{2}=0\]

7
Factor out the common term \(4m\).
\[4m(2-m)=0\]

8
Solve for \(m\).
\[m=0,2\]

Done
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