https://file.aiquickdraw.com/mathbot/file/1726348912759cksmjg96.jpg

The inequality in the image is:

\[
-4(w - 10) \leq 4w - 36
\]

### Step 1: Distribute the \(-4\) on the left-hand side:
\[
-4w + 40 \leq 4w - 36
\]

### Step 2: Move all terms involving \(w\) to one side by adding \(4w\) to both sides:
\[
40 \leq 8w - 36
\]

### Step 3: Move the constant terms to the other side by adding \(36\) to both sides:
\[
40 + 36 \leq 8w
\]
\[
76 \leq 8w
\]

### Step 4: Solve for \(w\) by dividing both sides by 8:
\[
w \geq \frac{76}{8}
\]
\[
w \geq 9.5
\]

### Final Answer:
\[
w \geq 9.5
\]

This means that \(w\) must be greater than or equal to \(9.5\).

Would you like further details or have any questions?

Here are 5 related questions:
1. How would the solution change if the inequality sign was reversed?
2. What happens if we substitute \(w = 9.5\) into the original inequality?
3. How would you graph this solution on a number line?
4. Can you explain why dividing by a negative number reverses the inequality?
5. What if the coefficient of \(w\) on the right side was a negative value?

**Tip:** When solving inequalities, always pay attention to the sign of the coefficient you're dividing by. If it's negative, the inequality direction must be reversed.

Solve the inequality: -4(w - 10) ≤ 4w - 36

Learn how to solve the linear inequality -4(w - 10) ≤ 4w - 36 with a detailed step-by-step solution. This problem involves key algebraic concepts, including distribution, transposing terms, and solving inequalities. Suitable for students in Grades 8-10.

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