Problem of the Week

Updated at Jul 26, 2021 11:02 AM

How would you solve \(6{(\frac{n-3}{2})}^{2}=6\)?

Below is the solution.



\[6{(\frac{n-3}{2})}^{2}=6\]

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

2
Simplify  \({2}^{2}\)  to  \(4\).
\[6\times \frac{{(n-3)}^{2}}{4}=6\]

3
Simplify  \(6\times \frac{{(n-3)}^{2}}{4}\)  to  \(\frac{3{(n-3)}^{2}}{2}\).
\[\frac{3{(n-3)}^{2}}{2}=6\]

4
Multiply both sides by \(2\).
\[3{(n-3)}^{2}=6\times 2\]

5
Simplify  \(6\times 2\)  to  \(12\).
\[3{(n-3)}^{2}=12\]

6
Divide both sides by \(3\).
\[{(n-3)}^{2}=\frac{12}{3}\]

7
Simplify  \(\frac{12}{3}\)  to  \(4\).
\[{(n-3)}^{2}=4\]

8
Take the square root of both sides.
\[n-3=\pm \sqrt{4}\]

9
Since \(2\times 2=4\), the square root of \(4\) is \(2\).
\[n-3=\pm 2\]

10
Break down the problem into these 2 equations.
\[n-3=2\]
\[n-3=-2\]

11
Solve the 1st equation: \(n-3=2\).
\[n=5\]

12
Solve the 2nd equation: \(n-3=-2\).
\[n=1\]

13
Collect all solutions.
\[n=5,1\]

Done
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