To solve the equation \( |2c - 13| = 6 \), follow these steps:

### Step 1: Set up two equations from the absolute value definition.

Since \( |x| = a \) means \( x = a \) or \( x = -a \), we can split the equation into two cases:

1. \( 2c - 13 = 6 \)
2. \( 2c - 13 = -6 \)

### Step 2: Solve each case.

**Case 1:**

\[
2c - 13 = 6
\]

Add 13 to both sides:

\[
2c = 19
\]

Divide by 2:

\[
c = \frac{19}{2} \quad \text{or} \quad c = 9.5
\]

**Case 2:**

\[
2c - 13 = -6
\]

Add 13 to both sides:

\[
2c = 7
\]

Divide by 2:

\[
c = \frac{7}{2} \quad \text{or} \quad c = 3.5
\]

### Step 3: Final solution.

The two possible solutions are:

\[
c = 9.5 \quad \text{or} \quad c = 3.5
\]

Would you like a detailed explanation of the steps?

Here are 5 related questions to expand on this:
1. How do you solve absolute value equations with more complex expressions?
2. What are the properties of absolute value?
3. How do you handle absolute value inequalities like \( |x - 5| < 4 \)?
4. Can absolute value functions have no solution?
5. How can you graph an absolute value equation?

**Tip:** Always remember to check both cases when solving absolute value equations!

Learn how to solve the absolute value equation |2c - 13| = 6 with a step-by-step guide. This problem demonstrates key algebra concepts, including how to split absolute value equations into two linear cases. Suitable for students in Grades 6-8.

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