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.

Learn how to solve the absolute value equation ∣2−2x∣−6=0 with a step-by-step breakdown. This algebra problem involves isolating the absolute value and solving two linear equations. Ideal for students in Grades 8-10.

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