Problem of the Week

Updated at Jun 12, 2023 2:07 PM

How would you solve the equation \(\frac{5}{3-4{x}^{2}}=-\frac{5}{97}\)?

Below is the solution.



\[\frac{5}{3-4{x}^{2}}=-\frac{5}{97}\]

1
Multiply both sides by \(3-4{x}^{2}\).
\[5=-\frac{5}{97}(3-4{x}^{2})\]

2
Simplify  \(\frac{5}{97}(3-4{x}^{2})\)  to  \(\frac{5(3-4{x}^{2})}{97}\).
\[5=-\frac{5(3-4{x}^{2})}{97}\]

3
Multiply both sides by \(97\).
\[5\times 97=-5(3-4{x}^{2})\]

4
Simplify  \(5\times 97\)  to  \(485\).
\[485=-5(3-4{x}^{2})\]

5
Divide both sides by \(-5\).
\[-\frac{485}{5}=3-4{x}^{2}\]

6
Simplify  \(\frac{485}{5}\)  to  \(97\).
\[-97=3-4{x}^{2}\]

7
Subtract \(3\) from both sides.
\[-97-3=-4{x}^{2}\]

8
Simplify  \(-97-3\)  to  \(-100\).
\[-100=-4{x}^{2}\]

9
Divide both sides by \(-4\).
\[\frac{-100}{-4}={x}^{2}\]

10
Two negatives make a positive.
\[\frac{100}{4}={x}^{2}\]

11
Simplify  \(\frac{100}{4}\)  to  \(25\).
\[25={x}^{2}\]

12
Take the square root of both sides.
\[\pm \sqrt{25}=x\]

13
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[\pm 5=x\]

14
Switch sides.
\[x=\pm 5\]

Done
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