You solved the inequality $\displaystyle{\left|{2}{z}+{4}\right|}\le{8}\usepackage{cmbright}\Huge\$ , instead of $\displaystyle{\left|{2}{z}+{4}\right|}\geq{8}\usepackage{cmbright}\Huge\$ . If $\displaystyle{\left|{X}\right|}\ge{8}\usepackage{cmbright}\Huge\$ , then $\displaystyle{X}\ge{8}\usepackage{cmbright}\Huge\$ or $\displaystyle{X}\le-{8}\usepackage{cmbright}\Huge\$ . In this problem X is $\displaystyle{2}{z}+{4}\usepackage{cmbright}\Huge\$ . This means that you have to solve two inequalities: $\displaystyle{2}{z}+{4}\ge{8}\usepackage{cmbright}\Huge\$ and $\displaystyle{2}{z}+{4}\le-{8}\usepackage{cmbright}\Huge\$ .