The equation \( |3a + 2| = -4 \) has no solution.

This is because the absolute value of any expression is always non-negative (i.e., greater than or equal to zero). Therefore, it is impossible for the absolute value of \(3a + 2\) to be equal to a negative number like \(-4\).

Thus, there is no value of \(a\) that satisfies the equation.

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. What are the general steps for solving absolute value equations?
2. How do you handle absolute value inequalities?
3. Can an absolute value expression ever be negative?
4. What if the equation was \( |3a + 2| = 4 \)? How would you solve it?
5. How does graphing an absolute value function help visualize its solutions?

**Tip:** Absolute value equations can have zero, one, or two solutions, depending on the values and setup.

Explore why the absolute value equation |3a + 2| = -4 has no solution. This problem highlights the key concept that absolute value expressions are always non-negative. Suitable for students in Grades 7-9.

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