To solve the equation \((x + 16)29 = 7\), we first need to isolate the term involving \(x\).
- Divide both sides of the equation by 29:
\[ x + 16 = \frac{7}{29} \]
- Next, we isolate \(x\) by subtracting 16 from both sides:
\[ x = \frac{7}{29} - 16 \]
- To combine \(\frac{7}{29}\) and \(-16\), we can convert \(-16\) into a fraction with a denominator of 29:
\[ -16 = -\frac{16 \times 29}{29} = -\frac{464}{29} \]
- Now, substituting this back into our equation gives:
\[ x = \frac{7}{29} - \frac{464}{29} \]
- This simplifies to:
\[ x = \frac{7 - 464}{29} = \frac{-457}{29} \]
- Finally, calculating \(-457 \div 29\):
\[ x \approx -15.762068965517241 \]
Rounding to the nearest hundredth, we get:
\[ x \approx -15.76 \]
Thus, the solution to the equation is
\[ \boxed{-15.76} \]
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