To solve the equation $|8x - 2| = 6$, we need to consider both the positive and negative scenarios of the absolute value.

1. Case 1: $8x - 2 = 6$ $8x = 8$ $x = 1$

2. Case 2: $8x - 2 = -6$ $8x = -4$ $x = -\frac{1}{2}$

So, the solutions are: $x = 1 \quad \text{or} \quad x = -\frac{1}{2}$

Would you like further explanation, or do you have any questions?

1. How does the absolute value impact equations?
2. What if the absolute value equation had no solutions?
3. How do you solve absolute value inequalities?
4. What happens if we add constants on both sides of an absolute value equation?
5. How do you graph solutions to absolute value equations?

Tip: Always consider both positive and negative cases for absolute value equations.