The given equation is:

$|2x - 6| = 8$

To solve this, we need to break it into two cases since the absolute value can be either positive or negative.

Case 1:

$2x - 6 = 8$ Solve for $x$:

$2x = 8 + 6 = 14$ $x = \frac{14}{2} = 7$

Case 2:

$2x - 6 = -8$ Solve for $x$:

$2x = -8 + 6 = -2$ $x = \frac{-2}{2} = -1$

Thus, the two solutions are: $x = 7 \quad \text{and} \quad x = -1$

The correct answers are $7$ and $-1$.

Would you like further details on absolute value equations or have any questions?

Related questions:

1. What are absolute value properties and how are they applied in solving equations?
2. Can absolute value equations ever have no solutions?
3. How do we graph absolute value equations?
4. What happens if the equation involves a quadratic within the absolute value?
5. How do we check if the solutions are correct by substitution?

Tip: When solving absolute value equations, always remember to consider both the positive and negative cases.