The problem to solve is:

$7(x - 10) - 2(x + 5) = 4x - 7 + 6x - 3$

Let's solve this step by step:

1. Distribute:

   • $7(x - 10) = 7x - 70$
   • $-2(x + 5) = -2x - 10$
   • $4x - 7 + 6x - 3 = 10x - 10$

   The equation becomes: $7x - 70 - 2x - 10 = 10x - 10$

2. Combine like terms:

   • On the left side: $7x - 2x - 70 - 10 = 5x - 80$
   • The equation becomes: $5x - 80 = 10x - 10$

3. Move variables to one side:

   • Subtract $5x$ from both sides: $-80 = 5x - 10$

4. Isolate $x$:

   • Add 10 to both sides: $-70 = 5x$
   • Divide by 5: $x = -14$

The solution is: $x = -14$

Let me know if you want further clarification or have specific questions. Here are related follow-up questions:

1. Can you verify if the distribution step makes sense to you?
2. Do you want an explanation of how combining like terms works in detail?
3. Would you like additional examples of solving multi-step equations?
4. Are there any particular steps you find tricky and want further explanation?
5. Would you like to know how this type of problem might appear in real-world applications?

Tip: Always double-check