Solve using the addition and multiplication principles. \( 4-8 y-3 y<92 \) Select the correct choice below and fill in the answer box within your choice. (Simplify your answer.) A. The solution set is \( \{y \mid y \geq \square\} \). B. The solution set is \( \{y \mid y \leq \square\} \). C. The solution set is \( \{y \mid y<\square\} \). D. The solution set is \( \{y \mid y>\square\} \).

To solve the inequality \( 4 - 8y - 3y < 92 \), we start by combining like terms: 1. Combine the \(y\) terms: \(-8y - 3y = -11y\) So the inequality becomes: \(4 - 11y < 92\) 2. Next, subtract 4 from both sides: \(-11y < 92 - 4\) \(-11y < 88\) 3. Now, divide both sides by -11. Remember, when dividing by a negative number, we reverse the inequality sign: \(y > \frac{88}{-11}\) \(y > -8\) Thus, the solution set is \( \{y \mid y > -8\} \), which corresponds to option D. First additional information: Did you know that the principle of solving inequalities follows similar rules as solving equations? The only catch is the direction of the inequality sign must be reversed whenever you multiply or divide both sides by a negative number! This little twist can trip you up, but it’s essential for getting the correct solution. Second additional information: Inequalities can be a part of real-world situations, like determining how many units of a product you can produce given the constraints of time and resources. For instance, if you know producing a toy takes 11 hours and you want to produce more than a certain quantity, you can use inequalities to plan your production schedule effectively. It's like saving time by being smart about your resources!