What is the solution set of the equation 12∣5x−15∣=10
 ?
A.{4}

B.{7}

C.{2, 4}

D.{−1, 7}


To solve the equation \(12 |5x - 15| = 10\), let's go through each step:

1. **Isolate the absolute value expression**:  
   Divide both sides by 12:
   \[
   |5x - 15| = \frac{10}{12} = \frac{5}{6}
   \]

2. **Set up two equations** (since the absolute value can be positive or negative):
   \[
   5x - 15 = \frac{5}{6} \quad \text{and} \quad 5x - 15 = -\frac{5}{6}
   \]

3. **Solve each equation**:

   - For \(5x - 15 = \frac{5}{6}\):
     \[
     5x = \frac{5}{6} + 15 = \frac{5}{6} + \frac{90}{6} = \frac{95}{6}
     \]
     \[
     x = \frac{95}{6 \cdot 5} = \frac{95}{30} = \frac{19}{6} \approx 3.17
     \]

   - For \(5x - 15 = -\frac{5}{6}\):
     \[
     5x = -\frac{5}{6} + 15 = -\frac{5}{6} + \frac{90}{6} = \frac{85}{6}
     \]
     \[
     x = \frac{85}{6 \cdot 5} = \frac{85}{30} = \frac{17}{6} \approx 2.83
     \]

4. **Check if these values are in the answer choices**. None of the answer choices directly match the solution set found. Double-check if there's a different interpretation.

Thus, none of the provided options A, B, C, or D match

What is the solution set of the equation 12∣5x−15∣=10? 
A.{4} 
B.{7} 
C.{2, 4} 
D.{−1, 7}

Explore the step-by-step solution to find the solution set of the equation 12∣5x−15∣=10, covering absolute value properties and techniques to solve equations with absolute values. Suitable for students in Grades 9-10.

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