What is the solution set of the equation 12∣5x−15∣=1012∣5x−15∣=10 ?

A.{4}{4}

B.{7}{7}

C.{2, 4}{2, 4}

D.{−1, 7}{−1, 7}


Let's solve the equation:

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

### Step 1: Isolate the absolute value.
Divide both sides by 12:

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

### Step 2: Handle the absolute value.
The expression \( |5x - 15| = \frac{5}{6} \) has two solutions:

\[
5x - 15 = \frac{5}{6} \quad \text{or} \quad 5x - 15 = -\frac{5}{6}
\]

### Step 3: Solve each equation.

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

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

Convert 15 to a fraction with the same denominator:

\[
15 = \frac{90}{6}, \quad \text{so} \quad 5x = \frac{90}{6} + \frac{5}{6} = \frac{95}{6}
\]

Now, divide by 5:

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

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

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

Convert 15 to a fraction with the same denominator:

\[
15 = \frac{90}{6}, \quad \text{so} \quad 5x = \frac{90}{6} - \frac{5}{6} = \frac{85}{6}
\]

Now, divide by 5:

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

### Step 4: Evaluate the solutions.

The two solutions we found are:

\[
x = \frac{19}{6} \quad \text{and} \quad x = \frac{17}{6}
\]

However, none of these solutions match the provided answer options.

---

It seems like there may be an error in the provided options. Please double-check the question or ask for clarification if needed. Would you like me to verify further steps or interpret differently?

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

This step-by-step solution covers solving the absolute value equation 12|5x - 15| = 10. Key concepts include handling absolute value, isolating terms, and solving linear equations. Suitable for high school students (Grades 9-12).

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation