## Elementary Algebra

$x=\dfrac{2}{3}$
Multiplying both sides by the $LCD= 9 ,$ the value of the variable that satisfies the given equation, $\dfrac{x-5}{3}+2=\dfrac{5}{9} ,$ is \begin{array}{l}\require{cancel} 3(x-5)+9(2)=1(5) \\\\ 3x-15+18=5 \\\\ 3x=5+15-18 \\\\ 3x=2 \\\\ x=\dfrac{2}{3} .\end{array}