$a)\frac{1}{2}\left(3a-2\right)=\frac{1}{2}\cdot 3a+\frac{1}{2}\cdot \left(-2\right)=\frac{3}{2}a-1$

$b)\frac{2}{3}\left(1,5+3x\right)=\frac{2}{{\sout{3}}^1}\cdot {\sout{1,5}}^{0,5}+\frac{2}{{\sout{3}}^1}\cdot {\sout{3}}^{1}x=1+2x$

$c)k\left(3l+2m\right)=3kl+2km$

$d)-p\left(r-5s\right)=-pr+5ps$