Answer:
[tex]\huge\boxed{x=\dfrac{13}{6}=2\dfrac{1}{6}}[/tex]
Step-by-step explanation:
[tex]\text{Convert mixed numbers to the improper fractions}\\\\6\dfrac{1}{4}=\dfrac{(6)(4)+1}{4}=\dfrac{25}{4}\\\\9\dfrac{3}{8}=\dfrac{(9)(8)+3}{8}=\dfrac{75}{8}\\\\6\dfrac{1}{4}\left(x-\dfrac{2}{3}\right)=9\dfrac{3}{8}\to\dfrac{25}{4}\left(x-\dfrac{2}{3}\right)=\dfrac{75}{8}\qquad\text{use the distributive property}\\\\\left(\dfrac{25}{4}\right)(x)-\left(\dfrac{25}{4}\right)\left(\dfrac{2}{3}\right)=\dfrac{75}{8}\\\\\dfrac{25}{4}x-\dfrac{50}{12}=\dfrac{75}{8}[/tex]
[tex]\dfrac{25}{4}x-\dfrac{25}{6}=\dfrac{75}{8}\qquad\text{multiply both sides by LCD = 24}\\\\24\cdot\dfrac{25}{4}x-24\cdot\dfrac{25}{6}=24\cdot\dfrac{75}{8}\\\\(6)(25)x-(4)(25)=(3)(75)\\\\150x-100=225\qquad\text{add 100 from both sides}\\\\150x=325\qquad\text{divide both sides by 150}\\\\x=\dfrac{325}{150}\\\\x=\dfrac{325:25}{150:25}\\\\x=\dfrac{13}{6}[/tex]
