## Elementary Algebra

$x\gt\dfrac{4}{3}$
Multiplying both sides by the $LCD= 30$ and then using the properties of inequalities, the solution to the given inequality, $\dfrac{3x}{5}-\dfrac{2}{3}\gt\dfrac{x}{10} ,$ is \begin{array}{l}\require{cancel} 6(3x)-10(2)\gt3(x) \\\\ 18x-20\gt3x \\\\ 18x-3x-20 \gt0 \\\\ 18x-3x\gt20 \\\\ 15x\gt20 \\\\ x\gt\dfrac{4}{3} .\end{array}