https://file.aiquickdraw.com/mathbot/file/1726349011960fbidue5e.jpg

Let's solve the given inequality step by step. The inequality from 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: Add \(4w\) to both sides to eliminate the \(-4w\) terms

\[
40 \leq -36
\]

### Step 3: Simplification

At this point, we have:

\[
40 \leq -36
\]

This statement is **false** because \(40\) is greater than \(-36\), not less than or equal to it.

### Conclusion

Since the inequality results in a false statement, the original inequality has **no solution**.

Would you like any further details or clarifications?

Here are 5 related questions to deepen your understanding:
1. How do you solve inequalities with variables on both sides?
2. What does it mean when an inequality has no solution?
3. How do you handle inequalities involving multiplication by negative numbers?
4. How do you graph the solution set of an inequality?
5. What is the difference between solving equations and inequalities?

**Tip:** When solving inequalities, if you multiply or divide both sides by a negative number, don't forget to flip the inequality sign!

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

Learn how to solve the linear inequality -4(w - 10) ≤ -4w - 36 step by step, covering key algebraic concepts such as the distributive property and handling inequalities with variables on both sides. Suitable for students in Grades 8-10.

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