Problem of the Week

Updated at Nov 2, 2026 3:32 PM

How would you solve \(5+\frac{6}{{(\frac{5}{q})}^{2}}=11\)?

Below is the solution.



\[5+\frac{6}{{(\frac{5}{q})}^{2}}=11\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[5+\frac{6}{\frac{{5}^{2}}{{q}^{2}}}=11\]

2
Simplify  \({5}^{2}\)  to  \(25\).
\[5+\frac{6}{\frac{25}{{q}^{2}}}=11\]

3
Invert and multiply.
\[5+6\times \frac{{q}^{2}}{25}=11\]

4
Simplify  \(6\times \frac{{q}^{2}}{25}\)  to  \(\frac{6{q}^{2}}{25}\).
\[5+\frac{6{q}^{2}}{25}=11\]

5
Subtract \(5\) from both sides.
\[\frac{6{q}^{2}}{25}=11-5\]

6
Simplify  \(11-5\)  to  \(6\).
\[\frac{6{q}^{2}}{25}=6\]

7
Multiply both sides by \(25\).
\[6{q}^{2}=6\times 25\]

8
Simplify  \(6\times 25\)  to  \(150\).
\[6{q}^{2}=150\]

9
Divide both sides by \(6\).
\[{q}^{2}=\frac{150}{6}\]

10
Simplify  \(\frac{150}{6}\)  to  \(25\).
\[{q}^{2}=25\]

11
Take the square root of both sides.
\[q=\pm \sqrt{25}\]

12
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[q=\pm 5\]

Done
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