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The equation to solve is:

\[
|5x - 4| = 12
\]

To solve an absolute value equation, we must consider two cases:

### Case 1: 
\[
5x - 4 = 12
\]

Solve for \(x\):

\[
5x = 12 + 4 \implies 5x = 16 \implies x = \frac{16}{5}
\]

### Case 2: 
\[
5x - 4 = -12
\]

Solve for \(x\):

\[
5x = -12 + 4 \implies 5x = -8 \implies x = -\frac{8}{5}
\]

### Solutions:
The solutions to the equation are:

\[
x = \frac{16}{5} \quad \text{and} \quad x = -\frac{8}{5}
\]

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you solve an absolute value inequality?
2. What are the steps to graph the function \(y = |5x - 4|\)?
3. How can you verify the solutions to an absolute value equation?
4. What happens if the right-hand side of the equation is negative, e.g., \(|5x - 4| = -12\)?
5. How do absolute value equations change when they involve a quadratic expression?

**Tip:** Always check both possible cases when solving absolute value equations to ensure you capture all potential solutions.

This page explains how to solve the absolute value equation |5x - 4| = 12. Learn the step-by-step approach, including handling two cases (5x - 4 = 12 and 5x - 4 = -12), and solving for x. Suitable for students in Grades 9-11.

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