The numbers $x+5,14, x$, and 5 have an average of 9 . What is the value of $x$ ?

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There are four numbers in total, so their average is

$$
\frac{(x+5)+14+x+5}{4}=\frac{2 x+24}{4}=\frac{x+12}{2} .
$$

The average is 9 , so $\frac{x+12}{2}=9$ or $x+12=18$ which means $x=6$.