Let's solve the expression step by step:

\[
-15x(3 + 7) + 43 - 86
\]

1. **Evaluate the expression inside the parentheses:**
   \[
   3 + 7 = 10
   \]
   So the expression becomes:
   \[
   -15x(10) + 43 - 86
   \]

2. **Multiply \(-15x\) by \(10\):**
   \[
   -15 \times 10 = -150
   \]
   So the expression now is:
   \[
   -150 + 43 - 86
   \]

3. **Add \(43\) to \(-150\):**
   \[
   -150 + 43 = -107
   \]
   So the expression is:
   \[
   -107 - 86
   \]

4. **Subtract \(86\) from \(-107\):**
   \[
   -107 - 86 = -193
   \]

The final result is:

\[
\boxed{-193}
\]

Would you like more details or have any questions about this? Here are 5 related questions you could explore:

1. What would happen if you replaced the number \(43\) with another number in the expression?
2. How does the order of operations affect solving this problem?
3. Can you create a similar expression and solve it?
4. What if the sign of \(x\) were positive? How would that change the result?
5. How does the distributive property work in expressions like this?

**Tip:** Always follow the order of operations (PEMDAS) when solving mathematical expressions to ensure accuracy.

Learn how to solve the algebraic expression -15x(3+7)+43-86 with a detailed step-by-step guide. This problem explores key algebraic concepts like the distributive property and the order of operations, suitable for students in Grades 6-8.

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