Let's solve the equation:

\[
-3u + 7 = -9u + 49
\]

### Step 1: Move the terms involving \( u \) to one side
Add \( 9u \) to both sides to get rid of the \( -9u \) on the right side:

\[
-3u + 9u + 7 = 49
\]

Simplifying:

\[
6u + 7 = 49
\]

### Step 2: Move the constant to the other side
Subtract \( 7 \) from both sides to isolate the term with \( u \):

\[
6u = 49 - 7
\]

Simplifying:

\[
6u = 42
\]

### Step 3: Solve for \( u \)
Divide both sides by 6:

\[
u = \frac{42}{6} = 7
\]

### Final Answer:
\[
u = 7
\]

Would you like further details or explanations?

Here are 5 related questions to expand on this topic:
1. What if the equation had fractions, how would you solve it?
2. How can you check if your solution is correct?
3. How would you solve if there were more variables involved?
4. Can you solve similar equations with absolute values?
5. What happens if the equation has no solution?

**Tip:** When solving linear equations, always move variables to one side and constants to the other for easier simplification.

Explore how to solve the linear equation -3u + 7 = -9u + 49 through a step-by-step process. This problem focuses on variable isolation and the application of properties of equality, making it suitable for students in Grades 6-8.

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