Answer:
[tex]\large\boxed{x=\dfrac{23}{33}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ x=0.\overline{69}\\\\x=0.696969...\qquad\text{multiply both sides by 100}\\\\100x=69.696969...\qquad\text{subtract}\ x\ \text{from}\ 100x:\\\\100x-x=69.696969...-0.696969...\\\\99x=69\qquad\text{divide both sides by 99}\\\\x=\dfrac{69}{99}\\\\x=\dfrac{23}{33}[/tex]
