Correct. One way to solve this equation is to rewrite the fractions to have the common denominator 18. Then the numerators must be equal:

$\displaystyle\frac{{{x}-{3}}}{{18}}=\frac{{4}}{{9}}\cdot\frac{{2}}{{2}}\usepackage{cmbright}\Huge\$

$\displaystyle\frac{{{x}-{3}}}{{18}}=\frac{{8}}{{18}}\usepackage{cmbright}\Huge\$

$\displaystyle{x}-{3}={8}\usepackage{cmbright}\Huge\$

$\displaystyle{x}={11}\usepackage{cmbright}\Huge\$