Let's solve the equation step by step.

The given equation is:

\[
-3(-7u + 9) - 2u = 7u - 35 - 2
\]

### Step 1: Distribute \(-3\) on the left-hand side.
\[
-3(-7u) + (-3)(9) - 2u = 7u - 35 - 2
\]
\[
21u - 27 - 2u = 7u - 35 - 2
\]

### Step 2: Combine like terms on both sides.
On the left side:
\[
21u - 2u - 27 = 7u - 35 - 2
\]
\[
19u - 27 = 7u - 37
\]

### Step 3: Get all terms involving \(u\) on one side of the equation and constants on the other side.
Subtract \(7u\) from both sides:
\[
19u - 7u - 27 = -37
\]
\[
12u - 27 = -37
\]

### Step 4: Add 27 to both sides to isolate the term with \(u\).
\[
12u = -37 + 27
\]
\[
12u = -10
\]

### Step 5: Divide both sides by 12 to solve for \(u\).
\[
u = \frac{-10}{12}
\]
\[
u = \frac{-5}{6}
\]

### Final Answer:
\[
u = -\frac{5}{6}
\]

Would you like more details on any step or have any questions?

Here are 5 related questions to deepen your understanding:
1. How would you solve a similar equation with different coefficients?
2. What happens if you change the sign in front of \(-3\) to a positive sign?
3. Can you solve the equation if all terms are fractions?
4. How does the distribution step change if the expression inside the parentheses is different?
5. How would the solution change if you had an additional variable in the equation?

**Tip:** Always check your solution by substituting it back into the original equation to ensure it satisfies the equation!

Learn how to solve the linear equation -3(-7u+9)-2u=7u-35-2 step-by-step with detailed explanations. This problem involves equations, distributive property, combining like terms, and is suitable for Grades 7-9.

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