Problem of the Week

Updated at Feb 11, 2019 4:37 PM

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Feb 11, 2019

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

Below is the solution.

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

Simplify \((4+4m)\times \frac{3-m}{5}\) to \(\frac{(4+4m)(3-m)}{5}\)

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

Factor out the common term \(4\)

\[\frac{4(1+m)(3-m)}{5}=\frac{12}{5}\]

Multiply both sides by \(5\)

\[4(1+m)(3-m)=12\]

Expand

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

Simplify \(12-4m+12m-4{m}^{2}\) to \(12+8m-4{m}^{2}\)

\[12+8m-4{m}^{2}=12\]

Cancel \(12\) on both sides

\[8m-4{m}^{2}=0\]

Factor out the common term \(4m\)

\[4m(2-m)=0\]

Solve for \(m\)

How?

\[m=0,2\]

Done