We are given the absolute value equation:

$|3x - 6| = 12$

To solve this, we need to consider two cases because the absolute value of an expression can be equal to a number if the expression inside is either positive or negative.

Case 1: $3x - 6 = 12$

Solve for $x$:

$3x - 6 = 12$

Add 6 to both sides:

$3x = 18$

Divide by 3:

$x = 6$

Case 2: $3x - 6 = -12$

Solve for $x$:

$3x - 6 = -12$

Add 6 to both sides:

$3x = -6$

Divide by 3:

$x = -2$

Thus, the solutions are $x = 6$ and $x = -2$.

Final Answer

The correct values of $x$ from the choices are:

• C. $x = -2$
• E. $x = 6$

Would you like further details or have any questions?

Here are five related questions to consider:

1. How do you solve absolute value equations with inequalities?
2. What are the general steps for solving equations involving absolute values?
3. What happens if the right-hand side of an absolute value equation is negative?
4. Can absolute value equations have more than two solutions?
5. How can you verify if a solution is correct?

Tip: Always check the two cases when solving absolute value equations!