https://file.aiquickdraw.com/mathbot/file/1725383889442d1c7l368.jpg

To determine which expressions are equivalent to \(-12m - 15\), let's simplify each option:

1. **\(-12m - 10 + 5\)**:
   \[
   -12m - 10 + 5 = -12m - 5
   \]
   This is not equivalent to \(-12m - 15\).

2. **\(-5m - 15 - 7m\)**:
   Combine like terms:
   \[
   -5m - 7m - 15 = -12m - 15
   \]
   This is equivalent to \(-12m - 15\).

3. **\(-3(4m - 5)\)**:
   Distribute the \(-3\):
   \[
   -3(4m - 5) = -12m + 15
   \]
   This is not equivalent to \(-12m - 15\).

4. **\(-3(4m + 5)\)**:
   Distribute the \(-3\):
   \[
   -3(4m + 5) = -12m - 15
   \]
   This is equivalent to \(-12m - 15\).

5. **\(4m - 8 = 16m - 7\)**:
   Simplify and compare both sides of the equation:
   \[
   4m - 8 = 16m - 7
   \]
   Rearranging, we get:
   \[
   -8 + 7 = 16m - 4m
   \]
   \[
   -1 = 12m
   \]
   This equation does not simplify to \(-12m - 15\), so it's not equivalent.

### Conclusion:
The equivalent expressions are:

- \(-5m - 15 - 7m\) 
- \(-3(4m + 5)\)

Would you like any details on these steps or have any questions?

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**Related Questions:**
1. How do you combine like terms in algebraic expressions?
2. How do you distribute multiplication over addition or subtraction in expressions?
3. What is the process for checking if two expressions are equivalent?
4. Can you explain the role of the distributive property in simplifying expressions?
5. How would the process change if the expressions included division?

**Tip:** When comparing algebraic expressions, always combine like terms and simplify as much as possible before making a comparison.

Which expressions are equivalent to -12m - 15?

Discover which expressions are equivalent to -12m - 15 by simplifying and combining like terms. This algebra problem helps students understand the use of distributive property and combining like terms. Suitable for students in Grades 7-8.

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