\[\frac{4x - 3}{5} - \frac{5x + 2}{3} \leq x + 3\ \ \ | \cdot 15\]
\[3(4x - 3) - 5(5x + 2) \leq 15(x + 3)\]
\[12x - 9 - 25x - 10 \leq 15x + 45\]
\[- 13x - 15x \leq 45 + 19\]
\[- 28x \leq 64\]
\[x \geq - \frac{28}{64}\]
\[x \geq - \frac{7}{16}.\]