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The equation you've provided is:

\[ 3(3 + 7k) + 10 < -86 \]

Let's solve this inequality step-by-step:

1. **Distribute the 3 inside the parentheses:**
   \[ 3(3 + 7k) = 9 + 21k \]

2. **Add 10 to both sides:**
   \[ 9 + 21k + 10 < -86 \]
   \[ 19 + 21k < -86 \]

3. **Subtract 19 from both sides:**
   \[ 21k < -86 - 19 \]
   \[ 21k < -105 \]

4. **Divide both sides by 21:**
   \[ k < \frac{-105}{21} \]
   \[ k < -5 \]

The solution to the inequality is \( k < -5 \).

Would you like further details on any of the steps, or do you have any other questions?

1. Would you like to see a graph of the inequality to visualize the solution?
2. How would the solution change if the inequality sign was reversed?
3. Do you want to learn how to check the solution using a test value?
4. Are you interested in understanding how to solve similar inequalities with different coefficients?
5. Can I help you

Learn how to solve the absolute value inequality 3|3 + 7k| + 10 < -86. This problem involves understanding the properties of absolute value and how it relates to inequalities. Suitable for students in Grades 9-12.

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