#### Answer

$x\ge2$

#### Work Step by Step

Remember that when we divide or multiply an inequality by a negative, we have to flip the sign of the inequality. Using the properties of inequality, the solution to the given inequality, $
\dfrac{2}{3}-\dfrac{x}{5}\le\dfrac{4}{15}
,$ is
\begin{array}{l}\require{cancel}
15\left( \dfrac{2}{3}-\dfrac{x}{5} \right)\le\left(\dfrac{4}{15} \right)15
\\\\
5(2)-3(x)\le4(1)
\\\\
10-3x\le4
\\\\
-3x\le4-10
\\\\
-3x\le-6
\\\\
x\ge\dfrac{-6}{-3}
\\\\
x\ge2
.\end{array}