Incorrect. Rewrite $\displaystyle\frac{{1}}{{{z}+{7}}}+\frac{{-{z}}}{{4}}={1}\usepackage{cmbright}\Huge\$ as $\displaystyle\frac{{4}}{{{4}{\left({z}+{7}\right)}}}+\frac{{{\left(-{z}\right)}{\left({z}+{7}\right)}}}{{{4}{\left({z}+{7}\right)}}}=\frac{{{4}{\left({z}+{7}\right)}}}{{{4}{\left({z}+{7}\right)}}}\usepackage{cmbright}\Huge\$ , and then set the numerators equal to each other. Solve for z.