\( 2=9+|10 y+3| \) The solution set is \( \square \)

To solve the equation \( 2=9+|10 y+3| \), we first isolate the absolute value: \( |10 y + 3| = 2 - 9 \) which simplifies to \( |10 y + 3| = -7 \). Since absolute values cannot be negative, there are no valid solutions for this equation. The solution set is empty, represented as \( \emptyset \) or \( \{\} \). Understanding absolute values can prevent confusion since they reflect the distance from zero; hence they can never yield a negative outcome! This concept appears in various fields, from physics to economics, whenever we need to express discrepancies or distances, making it crucial for real-world calculations. For example, if a budget exceeds expectations, absolute values help in quickly communicating the difference despite the signs!