Problem of the Week

Updated at Nov 26, 2018 4:52 PM

How would you solve the equation \(\frac{5}{3-\frac{5}{4x}}=\frac{20}{11}\)?

Below is the solution.



\[\frac{5}{3-\frac{5}{4x}}=\frac{20}{11}\]

1
Multiply both sides by \(3-\frac{5}{4x}\)
\[5=\frac{20}{11}(3-\frac{5}{4x})\]

2
Divide both sides by \(20\)
\[\frac{5}{20}=\frac{1}{11}(3-\frac{5}{4x})\]

3
Simplify \(\frac{5}{20}\) to \(\frac{1}{4}\)
\[\frac{1}{4}=\frac{1}{11}(3-\frac{5}{4x})\]

4
Simplify \(\frac{3-\frac{5}{4x}}{11}\) to \(\frac{3}{11}-\frac{\frac{5}{4x}}{11}\)
\[\frac{1}{4}=\frac{3}{11}-\frac{\frac{5}{4x}}{11}\]

5
Simplify \(\frac{\frac{5}{4x}}{11}\) to \(\frac{5}{4\times 11x}\)
\[\frac{1}{4}=\frac{3}{11}-\frac{5}{4\times 11x}\]

6
Simplify \(4\times 11x\) to \(44x\)
\[\frac{1}{4}=\frac{3}{11}-\frac{5}{44x}\]

7
Subtract \(\frac{3}{11}\) from both sides
\[\frac{1}{4}-\frac{3}{11}=-\frac{5}{44x}\]

8
Simplify \(\frac{1}{4}-\frac{3}{11}\) to \(-\frac{1}{44}\)
\[-\frac{1}{44}=-\frac{5}{44x}\]

9
Multiply both sides by \(44x\)
\[-\frac{1}{44}\times 44x=-5\]

10
Cancel \(44\)
\[-x=-5\]

11
Multiply both sides by \(-1\)
\[x=5\]

Done