https://file.aiquickdraw.com/mathbot/file/17253919951775fimcc50.jpg

Let's simplify the given expression step by step:

The expression is:

\[
-3(-4w - x) - 5(-5x - 6w)
\]

### Step 1: Distribute the -3 through the first parentheses
\[
-3(-4w - x) = -3 \times (-4w) - 3 \times (-x) = 12w + 3x
\]

### Step 2: Distribute the -5 through the second parentheses
\[
-5(-5x - 6w) = -5 \times (-5x) - 5 \times (-6w) = 25x + 30w
\]

### Step 3: Combine the simplified terms
\[
12w + 3x + 25x + 30w
\]

### Step 4: Combine like terms
\[
(12w + 30w) + (3x + 25x) = 42w + 28x
\]

Thus, the simplified expression is:

\[
42w + 28x
\]

If you have any questions or would like further details, let me know!

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Here are 5 related questions:
1. How do you simplify expressions with more variables?
2. Can you use factoring to simplify the expression further?
3. What are some common mistakes to avoid when distributing negatives?
4. How do you handle expressions with three or more terms inside parentheses?
5. How do you approach combining like terms in larger expressions?

**Tip:** Always be careful with signs when distributing through parentheses—negatives can easily be missed!

Learn how to simplify the algebraic expression -3(-4w - x) - 5(-5x - 6w) step by step using the distributive property. This tutorial covers key algebraic concepts, such as distribution and combining like terms. Suitable for students in Grades 7-9.

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