https://file.aiquickdraw.com/mathbot/file/1729368636049izglhdnr.jpg

Let's solve the equation step by step:

The given equation is:

\[
8u + 8 - 2(-4u - 2) = 2(u - 3)
\]

### Step 1: Distribute the terms
We first distribute the -2 on the left-hand side and the 2 on the right-hand side:

\[
8u + 8 + 8u + 4 = 2u - 6
\]

### Step 2: Combine like terms
Now, let's combine the terms on the left-hand side:

\[
(8u + 8u) + (8 + 4) = 2u - 6
\]
\[
16u + 12 = 2u - 6
\]

### Step 3: Move all terms involving \( u \) to one side
Subtract \( 2u \) from both sides:

\[
16u - 2u + 12 = -6
\]
\[
14u + 12 = -6
\]

### Step 4: Move the constant terms to the other side
Subtract 12 from both sides:

\[
14u = -6 - 12
\]
\[
14u = -18
\]

### Step 5: Solve for \( u \)
Now, divide both sides by 14:

\[
u = \frac{-18}{14} = \frac{-9}{7}
\]

### Final Answer:
\[
u = \frac{-9}{7}
\]

Would you like further details or have any questions about this solution?

Here are some related questions to deepen your understanding:
1. How do you simplify equations with distribution and combining like terms?
2. Why do we move all terms involving variables to one side of the equation?
3. What does dividing both sides by a number achieve when solving equations?
4. Can this method be applied to solve equations with fractions?
5. What happens if the equation had no solution or infinite solutions?

**Tip**: Always perform checks by substituting your solution back into the original equation to verify if both sides are equal.

Solve for u: 8u + 8 - 2(-4u - 2) = 2(u - 3)

Learn how to solve the algebraic equation 8u + 8 - 2(-4u - 2) = 2(u - 3) using distribution and simplification. This detailed step-by-step guide walks through combining like terms, moving variables to one side, and solving for u. Suitable for students in Grades 8-10.

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