https://file.aiquickdraw.com/mathbot/file/17272277048798gao7rog.jpg

The given equation is:

\[
8(2w - 1) - 4w = -116
\]

Let’s solve it step by step.

### Step 1: Distribute the 8 on the left-hand side
\[
8(2w) - 8(1) - 4w = -116
\]
This simplifies to:
\[
16w - 8 - 4w = -116
\]

### Step 2: Combine like terms
\[
(16w - 4w) - 8 = -116
\]
\[
12w - 8 = -116
\]

### Step 3: Add 8 to both sides to isolate the term with \(w\)
\[
12w = -116 + 8
\]
\[
12w = -108
\]

### Step 4: Divide both sides by 12 to solve for \(w\)
\[
w = \frac{-108}{12}
\]
\[
w = -9
\]

So, the solution is:
\[
w = -9
\]

Would you like more details or have any questions? Here are a few related questions to deepen understanding:

1. What would happen if you changed the -116 to a positive 116?
2. How can you check your solution after solving for \(w\)?
3. What is the importance of distributing properly in equations like this one?
4. How would the solution change if the coefficient of \(w\) was different in the original equation?
5. Can this process be applied to similar equations with different constants?

**Tip:** Always double-check by substituting your solution back into the original equation to ensure correctness!

Learn how to solve the linear equation 8(2w - 1) - 4w = -116 using distributive property and combining like terms. The step-by-step solution covers important algebraic concepts suitable for students in Grades 8-10.

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