Problem of the Week

Updated at Sep 18, 2023 11:42 AM

How can we solve the equation \(4(2+\frac{5}{{v}^{2}})=\frac{37}{4}\)?

Below is the solution.



\[4(2+\frac{5}{{v}^{2}})=\frac{37}{4}\]

1
Divide both sides by \(4\).
\[2+\frac{5}{{v}^{2}}=\frac{\frac{37}{4}}{4}\]

2
Simplify  \(\frac{\frac{37}{4}}{4}\)  to  \(\frac{37}{4\times 4}\).
\[2+\frac{5}{{v}^{2}}=\frac{37}{4\times 4}\]

3
Simplify  \(4\times 4\)  to  \(16\).
\[2+\frac{5}{{v}^{2}}=\frac{37}{16}\]

4
Subtract \(2\) from both sides.
\[\frac{5}{{v}^{2}}=\frac{37}{16}-2\]

5
Simplify  \(\frac{37}{16}-2\)  to  \(\frac{5}{16}\).
\[\frac{5}{{v}^{2}}=\frac{5}{16}\]

6
Multiply both sides by \({v}^{2}\).
\[5=\frac{5}{16}{v}^{2}\]

7
Simplify  \(\frac{5}{16}{v}^{2}\)  to  \(\frac{5{v}^{2}}{16}\).
\[5=\frac{5{v}^{2}}{16}\]

8
Multiply both sides by \(16\).
\[5\times 16=5{v}^{2}\]

9
Simplify  \(5\times 16\)  to  \(80\).
\[80=5{v}^{2}\]

10
Divide both sides by \(5\).
\[\frac{80}{5}={v}^{2}\]

11
Simplify  \(\frac{80}{5}\)  to  \(16\).
\[16={v}^{2}\]

12
Take the square root of both sides.
\[\pm \sqrt{16}=v\]

13
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[\pm 4=v\]

14
Switch sides.
\[v=\pm 4\]

Done
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