Let's solve the equation \(-4(x - 6) + 5 = -7(x + 4)\) step by step:

1. **Distribute the terms inside the parentheses**:
   \[
   -4 \cdot (x - 6) = -4x + 24 \quad \text{and} \quad -7 \cdot (x + 4) = -7x - 28
   \]
   So the equation becomes:
   \[
   -4x + 24 + 5 = -7x - 28
   \]

2. **Simplify the equation by combining like terms**:
   \[
   -4x + 29 = -7x - 28
   \]

3. **Add \(7x\) to both sides to move all the \(x\) terms to one side**:
   \[
   -4x + 7x + 29 = -28
   \]
   Simplifies to:
   \[
   3x + 29 = -28
   \]

4. **Subtract 29 from both sides**:
   \[
   3x = -28 - 29
   \]
   Simplifies to:
   \[
   3x = -57
   \]

5. **Divide both sides by 3**:
   \[
   x = \frac{-57}{3}
   \]
   Simplifies to:
   \[
   x = -19
   \]

So, the solution is \(x = -19\).

Would you like more details, or do you have any questions?

Here are some related questions you might find interesting:
1. How do you distribute negative numbers in equations?
2. What strategies can help solve equations with variables on both sides?
3. How can you verify your solution after solving an equation?
4. What are the steps for solving multi-step linear equations?
5. How can you handle equations with parentheses more effectively?

**Tip:** Distributing correctly is key! Always take care to distribute the sign along with the numbers.

Learn how to solve the equation -4(x - 6) + 5 = -7(x + 4) with a detailed step-by-step solution. This problem covers concepts such as linear equations and the distributive property. Suitable for students in Grades 7-9.

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