Answer:
[tex]\large\boxed{x=3\dfrac{7}{9}}[/tex]
Step-by-step explanation:
[tex]2\dfrac{1}{4}x=8\dfrac{1}{2}\qquad\text{convert the mixed numbers to the improper fractions}\\\\\dfrac{2\cdot4+1}{4}x=\dfrac{8\cdot2+1}{2}\\\\\dfrac{9}{4}x=\dfrac{17}{2}\qquad\text{multiply both sides by 4}\\\\4\!\!\!\!\diagup^1\cdot\dfrac{9}{4\!\!\!\!\diagup_1}x=4\!\!\!\!\diagup^2\cdot\dfrac{17}{2\!\!\!\!\diagup_1}\\\\9x=(2)(17)\\\\9x=34\qquad\text{divide both sides by 9}\\\\x=\dfrac{34}{9}\\\\x=3\dfrac{7}{9}[/tex]
