To simplify the expression:

\[
-5(6m + 3) - 7(-7m + 7)
\]

we distribute each term individually:

1. Start with \( -5(6m + 3) \):
   \[
   -5 \cdot 6m = -30m
   \]
   \[
   -5 \cdot 3 = -15
   \]
   So, \( -5(6m + 3) = -30m - 15 \).

2. Next, distribute \( -7(-7m + 7) \):
   \[
   -7 \cdot -7m = 49m
   \]
   \[
   -7 \cdot 7 = -49
   \]
   So, \( -7(-7m + 7) = 49m - 49 \).

Now, combine the terms:

\[
-30m - 15 + 49m - 49
\]

Combine like terms:

\[
(-30m + 49m) + (-15 - 49) = 19m - 64
\]

### Final Answer:
\[
19m - 64
\]

Would you like further clarification or have any questions?

---

1. How do you simplify expressions with multiple distributions?
2. What are like terms, and how do you identify them?
3. How would the solution change if the signs were different in the expression?
4. Can you apply similar steps to solve inequalities?
5. What are other methods to check if the simplification is correct?

**Tip:** When distributing negative numbers, be mindful of sign changes; this often causes common errors.

Master the steps to simplify the expression -5(6m + 3) - 7(-7m + 7) by applying distribution and combining like terms. This solution is ideal for students in Grades 7-9, reinforcing key algebraic skills with a step-by-step breakdown.

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