To solve the equation \(-4|k + 7| = 20\), follow these steps:

1. **Isolate the absolute value expression:**

   \[
   -4|k + 7| = 20
   \]

   Divide both sides by \(-4\) to isolate the absolute value:

   \[
   |k + 7| = \frac{20}{-4}
   \]

   \[
   |k + 7| = -5
   \]

2. **Analyze the absolute value result:**

   The absolute value of any expression can never be negative. Since the equation suggests \(|k + 7| = -5\), which is impossible, there is **no solution**.

**Final Answer:** The equation has no solution.

Would you like more details or have any questions?

Here are 5 related questions:

1. What are the properties of absolute value functions?
2. How do you determine when an absolute value equation has no solution?
3. Can an absolute value equation have a zero on one side?
4. How would you solve the equation \(-4|k + 7| = -20\)?
5. What if the equation was \(|k + 7| = 5\)?

**Tip:** Always remember that the absolute value of any real number is non-negative, so it can never equal a negative number.

Learn how to solve the equation -4|k + 7| = 20 with a step-by-step solution. Understand the properties of absolute value functions and how to isolate absolute value expressions. Suitable for students in Grades 9-12.

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