Problem of the Week

Updated at Apr 22, 2024 2:49 PM

To get more practice in equation, we brought you this problem of the week:

How would you solve the equation \({(\frac{5}{3-4p})}^{2}=25\)?

Check out the solution below!



\[{(\frac{5}{3-4p})}^{2}=25\]

1
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\frac{{5}^{2}}{{(3-4p)}^{2}}=25\]

2
Simplify  \({5}^{2}\)  to  \(25\).
\[\frac{25}{{(3-4p)}^{2}}=25\]

3
Multiply both sides by \({(3-4p)}^{2}\).
\[25=25{(3-4p)}^{2}\]

4
Divide both sides by \(25\).
\[1={(3-4p)}^{2}\]

5
Take the square root of both sides.
\[\pm \sqrt{1}=3-4p\]

6
Simplify  \(\sqrt{1}\)  to  \(1\).
\[\pm 1=3-4p\]

7
Switch sides.
\[3-4p=\pm 1\]

8
Break down the problem into these 2 equations.
\[3-4p=1\]
\[3-4p=-1\]

9
Solve the 1st equation: \(3-4p=1\).
\[p=\frac{1}{2}\]

10
Solve the 2nd equation: \(3-4p=-1\).
\[p=1\]

11
Collect all solutions.
\[p=\frac{1}{2},1\]

Done

Decimal Form: 0.5, 1
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