Problem of the Week

Updated at Nov 26, 2018 4:52 PM

How would you solve the equation 53−54x=2011\frac{5}{3-\frac{5}{4x}}=\frac{20}{11}?

Below is the solution.



53−54x=2011\frac{5}{3-\frac{5}{4x}}=\frac{20}{11}

1
Multiply both sides by 3−54x3-\frac{5}{4x}.
5=2011(3−54x)5=\frac{20}{11}(3-\frac{5}{4x})

2
Divide both sides by 2020.
520=111(3−54x)\frac{5}{20}=\frac{1}{11}(3-\frac{5}{4x})

3
Simplify  520\frac{5}{20}  to  14\frac{1}{4}.
14=111(3−54x)\frac{1}{4}=\frac{1}{11}(3-\frac{5}{4x})

4
Simplify  3−54x11\frac{3-\frac{5}{4x}}{11}  to  311−54x11\frac{3}{11}-\frac{\frac{5}{4x}}{11}.
14=311−54x11\frac{1}{4}=\frac{3}{11}-\frac{\frac{5}{4x}}{11}

5
Simplify  54x11\frac{\frac{5}{4x}}{11}  to  54×11x\frac{5}{4\times 11x}.
14=311−54×11x\frac{1}{4}=\frac{3}{11}-\frac{5}{4\times 11x}

6
Simplify  4×11x4\times 11x  to  44x44x.
14=311−544x\frac{1}{4}=\frac{3}{11}-\frac{5}{44x}

7
Subtract 311\frac{3}{11} from both sides.
14−311=−544x\frac{1}{4}-\frac{3}{11}=-\frac{5}{44x}

8
Simplify  14−311\frac{1}{4}-\frac{3}{11}  to  −144-\frac{1}{44}.
−144=−544x-\frac{1}{44}=-\frac{5}{44x}

9
Multiply both sides by 44x44x.
−144×44x=−5-\frac{1}{44}\times 44x=-5

10
Cancel 4444.
−x=−5-x=-5

11
Multiply both sides by −1-1.
x=5x=5

Done
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