Problem of the Week

Updated at Nov 2, 2020 3:42 PM

How can we solve the equation \(5\times \frac{6}{{(4x)}^{2}}=\frac{3}{40}\)?

Below is the solution.



\[5\times \frac{6}{{(4x)}^{2}}=\frac{3}{40}\]

1
Use Multiplication Distributive Property: \({(xy)}^{a}={x}^{a}{y}^{a}\).
\[5\times \frac{6}{{4}^{2}{x}^{2}}=\frac{3}{40}\]

2
Simplify  \({4}^{2}\)  to  \(16\).
\[5\times \frac{6}{16{x}^{2}}=\frac{3}{40}\]

3
Simplify  \(5\times \frac{6}{16{x}^{2}}\)  to  \(\frac{30}{16{x}^{2}}\).
\[\frac{30}{16{x}^{2}}=\frac{3}{40}\]

4
Simplify  \(\frac{30}{16{x}^{2}}\)  to  \(\frac{15}{8{x}^{2}}\).
\[\frac{15}{8{x}^{2}}=\frac{3}{40}\]

5
Multiply both sides by \(8{x}^{2}\).
\[15=\frac{3}{40}\times 8{x}^{2}\]

6
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[15=\frac{3\times 8{x}^{2}}{40}\]

7
Simplify  \(3\times 8{x}^{2}\)  to  \(24{x}^{2}\).
\[15=\frac{24{x}^{2}}{40}\]

8
Simplify  \(\frac{24{x}^{2}}{40}\)  to  \(\frac{3{x}^{2}}{5}\).
\[15=\frac{3{x}^{2}}{5}\]

9
Multiply both sides by \(5\).
\[15\times 5=3{x}^{2}\]

10
Simplify  \(15\times 5\)  to  \(75\).
\[75=3{x}^{2}\]

11
Divide both sides by \(3\).
\[\frac{75}{3}={x}^{2}\]

12
Simplify  \(\frac{75}{3}\)  to  \(25\).
\[25={x}^{2}\]

13
Take the square root of both sides.
\[\pm \sqrt{25}=x\]

14
Since \(5\times 5=25\), the square root of \(25\) is \(5\).
\[\pm 5=x\]

15
Switch sides.
\[x=\pm 5\]

Done
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