Let's solve the equation step by step:

The given equation is:
\[
3u + 4u - 29 = -71
\]

### Step 1: Combine like terms.
Combine the \(3u\) and \(4u\):
\[
(3u + 4u) = 7u
\]
Now the equation becomes:
\[
7u - 29 = -71
\]

### Step 2: Isolate the term with \(u\).
Add 29 to both sides to get rid of the constant on the left:
\[
7u = -71 + 29
\]
\[
7u = -42
\]

### Step 3: Solve for \(u\).
Divide both sides by 7:
\[
u = \frac{-42}{7}
\]
\[
u = -6
\]

### Final Answer:
\[
u = -6
\]

Would you like any further explanation on this solution? 

Here are five related questions you might want to explore:
1. What happens if one of the terms was negative, like \(3u - 4u - 29 = -71\)?
2. How would you solve \(5u + 6u - 40 = -90\)?
3. What if the equation involved fractions, like \(\frac{3u}{2} + \frac{4u}{3} - 29 = -71\)?
4. How can you verify the solution by substituting back into the original equation?
5. Can equations like these ever have no solution?

**Tip**: When combining like terms, always look out for signs (positive or negative) to avoid mistakes in simplification!

Learn how to solve the linear equation 3u + 4u - 29 = -71 with a clear, step-by-step solution. This problem covers essential algebraic concepts, including combining like terms and solving for a variable. Ideal for students in Grades 6-8.

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