Problem of the Week

Updated at Oct 19, 2026 3:03 PM

This week we have another equation problem:

How can we solve the equation \(\frac{4}{4\times \frac{5}{{x}^{2}}}=\frac{16}{5}\)?

Let's start!



\[\frac{4}{4\times \frac{5}{{x}^{2}}}=\frac{16}{5}\]

1
Simplify  \(4\times \frac{5}{{x}^{2}}\)  to  \(\frac{20}{{x}^{2}}\).
\[\frac{4}{\frac{20}{{x}^{2}}}=\frac{16}{5}\]

2
Invert and multiply.
\[4\times \frac{{x}^{2}}{20}=\frac{16}{5}\]

3
Simplify  \(4\times \frac{{x}^{2}}{20}\)  to  \(\frac{{x}^{2}}{5}\).
\[\frac{{x}^{2}}{5}=\frac{16}{5}\]

4
Multiply both sides by \(5\).
\[{x}^{2}=\frac{16}{5}\times 5\]

5
Cancel \(5\).
\[{x}^{2}=16\]

6
Take the square root of both sides.
\[x=\pm \sqrt{16}\]

7
Since \(4\times 4=16\), the square root of \(16\) is \(4\).
\[x=\pm 4\]

Done
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