Multiply both sides by 2:

$\displaystyle\frac{{-{3}{z}-{1}}}{{2}}\cdot{2}>{4}\cdot{2}\usepackage{cmbright}\Huge\$ or $\displaystyle-{3}{z}-{1}>{8}\usepackage{cmbright}\Huge\$

Add 1 to both sides:

$\displaystyle-{3}{z}-{1}+{1}>{8}+{1}\usepackage{cmbright}\Huge\$ or $\displaystyle-{3}{z}>{9}\usepackage{cmbright}\Huge\$

Divide both sides by $\displaystyle-{3}\usepackage{cmbright}\Huge\$ and reverse the inequality symbol:

$\displaystyle\frac{{-{3}{z}}}{{-{{3}}}}<\frac{{9}}{{-{{3}}}}\usepackage{cmbright}\Huge\$ or $\displaystyle{z}<-{3}\usepackage{cmbright}\Huge\$