Problem of the Week

Updated at Oct 12, 2020 10:33 AM

This week we have another equation problem:

How can we solve the equation \(6{(\frac{4}{4v})}^{2}=\frac{3}{2}\)?

Let's start!



\[6{(\frac{4}{4v})}^{2}=\frac{3}{2}\]

1
Cancel \(4\).
\[6{(\frac{1}{v})}^{2}=\frac{3}{2}\]

2
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[6\times \frac{1}{{v}^{2}}=\frac{3}{2}\]

3
Simplify  \(6\times \frac{1}{{v}^{2}}\)  to  \(\frac{6}{{v}^{2}}\).
\[\frac{6}{{v}^{2}}=\frac{3}{2}\]

4
Multiply both sides by \({v}^{2}\).
\[6=\frac{3}{2}{v}^{2}\]

5
Simplify  \(\frac{3}{2}{v}^{2}\)  to  \(\frac{3{v}^{2}}{2}\).
\[6=\frac{3{v}^{2}}{2}\]

6
Multiply both sides by \(2\).
\[6\times 2=3{v}^{2}\]

7
Simplify  \(6\times 2\)  to  \(12\).
\[12=3{v}^{2}\]

8
Divide both sides by \(3\).
\[\frac{12}{3}={v}^{2}\]

9
Simplify  \(\frac{12}{3}\)  to  \(4\).
\[4={v}^{2}\]

10
Take the square root of both sides.
\[\pm \sqrt{4}=v\]

11
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[\pm 2=v\]

12
Switch sides.
\[v=\pm 2\]

Done
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