Problem of the Week

Updated at Mar 2, 2020 10:03 AM

This week we have another equation problem:

How can we solve the equation \(\frac{q-3}{\frac{5}{q}}=-\frac{2}{5}\)?

Let's start!



\[\frac{q-3}{\frac{5}{q}}=-\frac{2}{5}\]

1
Invert and multiply.
\[(q-3)\times \frac{q}{5}=-\frac{2}{5}\]

2
Use this rule: \(a \times \frac{b}{c}=\frac{ab}{c}\).
\[\frac{(q-3)q}{5}=-\frac{2}{5}\]

3
Regroup terms.
\[\frac{q(q-3)}{5}=-\frac{2}{5}\]

4
Multiply both sides by \(5\).
\[q(q-3)=-2\]

5
Expand.
\[{q}^{2}-3q=-2\]

6
Move all terms to one side.
\[{q}^{2}-3q+2=0\]

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

8
Solve for \(q\).
\[q=2,1\]

Done
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