# 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 $$-1$$.$x=5$Donex=5