Answer:
[tex]\large\boxed{x=3\dfrac{9}{20}}[/tex]
Step-by-step explanation:
[tex]5\dfrac{1}{5}=x+1\dfrac{3}{4}\qquad\text{convert the mixed numbers to the improper fractions}\\\\\dfrac{5\cdot5+1}{5}=x+\dfrac{1\cdot4+3}{4}\\\\\dfrac{26}{5}=x+\dfrac{7}{4}\qquad\text{multiply both sides by LCM(5, 4) = 20}\\\\20\!\!\!\!\!\diagup^4\cdot\dfrac{26}{5\!\!\!\!\diagup_1}=20x+20\!\!\!\!\!\diagup^5\cdot\dfrac{7}{4\!\!\!\!\diagup_1}\\\\(4)(26)=20x+(5)(7)\\\\104=20x+35\qquad\text{subtract 35 from both sides}\\\\69=20x\qquad\text{divide both sides by 20}\\\\\dfrac{69}{20}=x\to x=3\dfrac{9}{20}[/tex]
