https://file.aiquickdraw.com/mathbot/file/17262757686039nkfbqqs.jpg

The inequality in the image is:

\[
-8 - 4(7w + 7) < 8w - 1 + 3w
\]

Let's solve this step by step:

### Step 1: Expand the expression on the left
Distribute the \(-4\) over \((7w + 7)\):

\[
-8 - 4(7w + 7) = -8 - 28w - 28
\]

So the inequality becomes:

\[
-8 - 28w - 28 < 8w - 1 + 3w
\]

### Step 2: Simplify both sides
Combine like terms on the left-hand side:

\[
-8 - 28 = -36
\]

Thus, the inequality is:

\[
-36 - 28w < 8w - 1 + 3w
\]

Now combine like terms on the right-hand side:

\[
8w + 3w = 11w
\]

So, the inequality is now:

\[
-36 - 28w < 11w - 1
\]

### Step 3: Move all terms involving \(w\) to one side
Add \(28w\) to both sides to move all \(w\) terms to the right-hand side:

\[
-36 < 11w - 1 + 28w
\]

Simplify:

\[
-36 < 39w - 1
\]

### Step 4: Isolate the variable \(w\)
Add 1 to both sides:

\[
-36 + 1 < 39w
\]

\[
-35 < 39w
\]

### Step 5: Solve for \(w\)
Divide both sides by 39:

\[
\frac{-35}{39} < w
\]

Thus, the solution is:

\[
w > \frac{-35}{39}
\]

We can simplify this fraction:

\[
w > \frac{-5}{7}
\]

### Final Answer:
\[
w > \frac{-5}{7}
\]

Do you want more details on any step? 

Here are 5 related questions you might find helpful:
1. How do you handle inequalities when multiplying or dividing by a negative number?
2. What is the significance of reversing the inequality sign?
3. How can inequalities be graphed on a number line?
4. What happens if both sides of an inequality are multiplied by the same value?
5. What are common mistakes made when solving multi-step inequalities?

**Tip**: Always double-check signs when solving inequalities, especially when distributing negative values!

This page explains how to solve the linear inequality -8 - 4(7w + 7) < 8w - 1 + 3w step by step using the distributive property and combining like terms. Learn the solution in detail, ideal for students in Grades 8-10.

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