What is the solution set of the equation 12∣5x−15∣=10

A.{4}

B.{7}

C.{2, 4}

D.{−1, 7}

We are given the equation:

\[
12|5x - 15| = 10
\]

### Step 1: Isolate the absolute value expression
First, divide both sides of the equation by 12 to isolate the absolute value term:

\[
|5x - 15| = \frac{10}{12} = \frac{5}{6}
\]

### Step 2: Solve the absolute value equation
We know that for any absolute value expression \( |A| = B \), the solutions are:

\[
A = B \quad \text{or} \quad A = -B
\]

In this case, \( A = 5x - 15 \) and \( B = \frac{5}{6} \). So, we need to solve two equations:

1. \( 5x - 15 = \frac{5}{6} \)
2. \( 5x - 15 = -\frac{5}{6} \)

### Step 3: Solve both equations

#### Equation 1: \( 5x - 15 = \frac{5}{6} \)
Add 15 to both sides:

\[
5x = \frac{5}{6} + 15 = \frac{5}{6} + \frac{90}{6} = \frac{95}{6}
\]

Now, divide both sides by 5:

\[
x = \frac{95}{6} \times \frac{1}{5} = \frac{95}{30} = \frac{19}{6}
\]

#### Equation 2: \( 5x - 15 = -\frac{5}{6} \)
Add 15 to both sides:

\[
5x = -\frac{5}{6} + 15 = -\frac{5}{6} + \frac{90}{6} = \frac{85}{6}
\]

Now, divide both sides by 5:

\[
x = \frac{85}{6} \times \frac{1}{5} = \frac{85}{30} = \frac{17}{6}
\]

### Step 4: Approximate solutions
- \( \frac{19}{6} \approx 3.17 \)
- \( \frac{17}{6} \approx 2.83 \)

### Step 5: Compare with the options
The solutions are approximately 3.17 and 2.83, but none of the options match this exactly. Let's consider simplifying the interpretation of the question. After re-evaluating, no distinct integers correspond closely to our calculated answers, suggesting a recheck might be needed for clarity.

What is the solution set of the equation 12∣5x−15∣=10?

Explore how to solve the absolute value equation 12∣5x−15∣=10. This step-by-step guide covers key algebraic concepts, including absolute value properties and solving linear equations. Suitable for students in Grades 9-11.

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