Let's simplify the expression step by step:

Given:  
\[ 10(x + 2) - 8(x - 7) \]

1. First, distribute the constants (10 and -8) to both terms inside the parentheses:

\[
10(x + 2) = 10x + 20
\]
\[
-8(x - 7) = -8x + 56
\]

2. Now, substitute these results back into the expression:

\[
10x + 20 - 8x + 56
\]

3. Combine like terms:

\[
(10x - 8x) + (20 + 56) = 2x + 76
\]

So, the simplified expression is:
\[
2x + 76
\]

Would you like a more detailed explanation or have any questions?

Here are 5 related questions you might explore:
1. What is the simplified form of \( 5(2x + 4) - 3(4x - 6) \)?
2. How would you solve the equation \( 2x + 76 = 100 \)?
3. What happens if the expression had fractions like \( \frac{1}{2}(x + 2) - \frac{1}{3}(x - 1) \)?
4. Can you simplify the expression \( 4x + 5(3x - 2) - 7x \)?
5. What is the result of \( 12(x + 3) - 9(x + 5) \)?

**Tip:** Always distribute and combine like terms carefully to avoid mistakes!

This guide walks you through simplifying the algebraic expression 10(x+2) - 8(x-7) step by step. Key concepts include applying the distributive property and combining like terms. Suitable for students in Grades 6-8 looking to strengthen their algebra skills.

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