Let's solve the expression \(-2(x + 7) - 8(5x + 4)\).

### Step-by-step:
1. Distribute \(-2\) to the terms inside the first parentheses:
   \[
   -2(x + 7) = -2x - 14
   \]

2. Distribute \(-8\) to the terms inside the second parentheses:
   \[
   -8(5x + 4) = -40x - 32
   \]

3. Combine all the terms together:
   \[
   -2x - 14 - 40x - 32
   \]

4. Combine like terms:
   \[
   (-2x - 40x) + (-14 - 32) = -42x - 46
   \]

So, the simplified expression is:
\[
-42x - 46
\]

Would you like further clarification or more details?

### Relative questions:
1. What is the distributive property, and how is it used in algebra?
2. Can you simplify expressions with fractions similarly?
3. What happens when you distribute a positive or negative number?
4. How do like terms affect the simplification of algebraic expressions?
5. Can you apply these steps to a different expression, such as \(3(2x + 5) - 4(x - 1)\)?

### Tip:
Always perform distribution carefully, ensuring that both constants and variables inside the parentheses are multiplied by the number outside.

Discover how to simplify the algebraic expression -2(x + 7) - 8(5x + 4) using the distributive property. This step-by-step guide walks through key algebra concepts like distributing terms and combining like terms. Perfect for students in Grades 6-8.

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