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 q−35q=−25\frac{q-3}{\frac{5}{q}}=-\frac{2}{5}?

Let's start!



q−35q=−25\frac{q-3}{\frac{5}{q}}=-\frac{2}{5}

1
Invert and multiply.
(q−3)×q5=−25(q-3)\times \frac{q}{5}=-\frac{2}{5}

2
Use this rule: a×bc=abca \times \frac{b}{c}=\frac{ab}{c}.
(q−3)q5=−25\frac{(q-3)q}{5}=-\frac{2}{5}

3
Regroup terms.
q(q−3)5=−25\frac{q(q-3)}{5}=-\frac{2}{5}

4
Multiply both sides by 55.
q(q−3)=−2q(q-3)=-2

5
Expand.
q2−3q=−2{q}^{2}-3q=-2

6
Move all terms to one side.
q2−3q+2=0{q}^{2}-3q+2=0

7
Factor q2−3q+2{q}^{2}-3q+2.
(q−2)(q−1)=0(q-2)(q-1)=0

8
Solve for qq.
q=2,1q=2,1

Done
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