IMAS 2020–2021 Junior Round 2 Question 7

For any real number $x$, we define $[x]$ to be the greatest integer that does not exceed $x$ and $\{x\}$ to be the fractional part of $x$ such that $\{x\}=x-[x]$. If $2[x]+3\{x\}=\frac{69}{5}$, then what is the value of $x$?