Problem of the Week

Updated at Aug 8, 2022 9:57 AM

How can we solve the equation \(\frac{{(4(y-3))}^{2}}{5}=\frac{16}{5}\)?

Below is the solution.



\[\frac{{(4(y-3))}^{2}}{5}=\frac{16}{5}\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[\frac{{4}^{2}{(y-3)}^{2}}{5}=\frac{16}{5}\]

2
Simplify  \({4}^{2}\)  to  \(16\).
\[\frac{16{(y-3)}^{2}}{5}=\frac{16}{5}\]

3
Multiply both sides by \(5\).
\[16{(y-3)}^{2}=\frac{16}{5}\times 5\]

4
Cancel \(5\).
\[16{(y-3)}^{2}=16\]

5
Divide both sides by \(16\).
\[{(y-3)}^{2}=1\]

6
Take the square root of both sides.
\[y-3=\pm \sqrt{1}\]

7
Simplify  \(\sqrt{1}\)  to  \(1\).
\[y-3=\pm 1\]

8
Break down the problem into these 2 equations.
\[y-3=1\]
\[y-3=-1\]

9
Solve the 1st equation: \(y-3=1\).
\[y=4\]

10
Solve the 2nd equation: \(y-3=-1\).
\[y=2\]

11
Collect all solutions.
\[y=4,2\]

Done
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