To solve the equation \((x + 16)29 = 7\), we first isolate \(x\) by dividing both sides by 29:
\[ x + 16 = \frac{7}{29} \]
Next, we subtract 16 from both sides to find \(x\):
\[ x = \frac{7}{29} - 16 \]
To combine these terms, we convert 16 into a fraction with a denominator of 29:
\[ 16 = \frac{16 \times 29}{29} = \frac{464}{29} \]
Now we can subtract the fractions:
\[ x = \frac{7}{29} - \frac{464}{29} = \frac{7 - 464}{29} = \frac{-457}{29} \]
Calculating the division gives:
\[ x \approx -15.76 \]
Rounding to the nearest hundredth, we find:
\[ \boxed{-15.76} \]