\(\left(2\frac{1}{2}x-\frac{5}{3}\right)^2=\frac{16}{9}\)
\(\left(\frac{5}{2}x-\frac{5}{3}\right)^2=\frac{4^2}{3^2}\)
\(\left(\frac{5}{2}x-\frac{5}{3}\right)^2=\left(\frac{4}{3}\right)^2\)
\(\frac{5}{2}x-\frac{5}{3}=\frac{4}{3}\)
\(\frac{5}{2}x=\frac{4}{3}+\frac{5}{3}\)
\(\frac{5}{2}x=\frac{9}{3}=3\)
\(x=3.\frac{5}{2}\)
\(x=\frac{15}{2}\)