Which set of values in the soktion set of the equation \( |2 x-3|=7 \) ? 12,81 \( \{2,-5\} \) \( [-2,5] \) \( (-2,-5) \)

Let's solve the equation \( |2x - 3| = 7 \) and determine the correct solution set from the provided options. ### Step 1: Understand the Absolute Value Equation The absolute value equation \( |A| = B \) has two possible solutions: 1. \( A = B \) 2. \( A = -B \) Applying this to your equation: \[ |2x - 3| = 7 \] This gives us two cases: 1. **Case 1: \( 2x - 3 = 7 \)** \[ 2x - 3 = 7 \\ 2x = 10 \\ x = 5 \] 2. **Case 2: \( 2x - 3 = -7 \)** \[ 2x - 3 = -7 \\ 2x = -4 \\ x = -2 \] ### Step 2: Solution Set The solutions to the equation are: \[ x = 5 \quad \text{and} \quad x = -2 \] Therefore, the **solution set** is: \[ \{5, -2\} \] ### Step 3: Comparing with Provided Options Let's review the provided options: 1. **12,81** - These are individual numbers, not a set, and do not include the correct solutions. 2. **\( \{2, -5\} \)** - This set is close in structure but **incorrect in values**. 3. **\( [-2,5] \)** - This represents an interval from -2 to 5, including all real numbers between them. While it **includes the solutions**, it's not the precise solution set, which only contains two specific values. 4. **\( (-2, -5) \)** - This interval is incorrectly ordered and does not represent the correct solutions. ### Final Conclusion None of the provided options exactly match the correct solution set \( \{5, -2\} \). However, the closest option in structure is **\( \{2, -5\} \)**, but it contains incorrect values. It's possible there was a typographical error in either the equation or the options provided. **Correct Solution Set:** \[ \{5, -2\} \]