To solve the equation $|2 - 2x| - 6 = 0$, let's proceed step by step.

Step 1: Isolate the absolute value expression

$|2 - 2x| - 6 = 0$ Add 6 to both sides: $|2 - 2x| = 6$

Step 2: Break down the absolute value equation

An absolute value equation $|A| = B$ means that $A$ can either be $B$ or $-B$. So we have two cases:

1. $2 - 2x = 6$
2. $2 - 2x = -6$

Step 3: Solve each case separately

Case 1: $2 - 2x = 6$

Subtract 2 from both sides: $-2x = 4$ Divide by -2: $x = -2$

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

Subtract 2 from both sides: $-2x = -8$ Divide by -2: $x = 4$

Step 4: Final solution

The solutions are $x = -2$ and $x = 4$.

Would you like more details or have any questions about this?

Here are five related questions to expand on this:

1. How do you solve inequalities with absolute values, such as $|x - 3| > 5$?
2. What are some common properties of absolute value functions?
3. How can absolute value functions be graphed on a coordinate plane?
4. How do absolute value equations with two absolute terms differ in solving methods?
5. What is the significance of absolute value in real-life applications?

Tip: Always check if the solutions satisfy the original equation when working with absolute values.