Solve the equation involving absolute value. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
|2x − 4| − 8 = −2

We need to solve the equation involving the absolute value:

\[
|2x - 4| - 8 = -2
\]

### Step 1: Isolate the absolute value term
First, isolate the absolute value by adding 8 to both sides of the equation:

\[
|2x - 4| = -2 + 8
\]
\[
|2x - 4| = 6
\]

### Step 2: Set up two cases
The absolute value equation \( |A| = B \) can be written as two separate equations:
1. \( 2x - 4 = 6 \)
2. \( 2x - 4 = -6 \)

### Step 3: Solve both cases

#### Case 1: \( 2x - 4 = 6 \)
Add 4 to both sides:
\[
2x = 10
\]
Divide by 2:
\[
x = 5
\]

#### Case 2: \( 2x - 4 = -6 \)
Add 4 to both sides:
\[
2x = -2
\]
Divide by 2:
\[
x = -1
\]

### Step 4: Final answer
The solutions to the equation are:
\[
x = 5, -1
\]

Would you like a detailed explanation of any particular step, or do you have further questions?

Here are 5 related questions for more practice:
1. Solve \( |3x + 7| - 5 = 2 \).
2. Solve \( |x + 4| = 0 \).
3. Solve \( 3|x - 1| = 9 \).
4. Solve \( |5x + 2| + 4 = 10 \).
5. Solve \( |x + 6| = 3x \).

**Tip**: When solving absolute value equations, always remember to set up two cases to capture all potential solutions.

Solve the equation involving absolute value. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) |2x − 4| − 8 = −2

Learn how to solve the absolute value equation |2x − 4| − 8 = −2 with a step-by-step explanation. This problem demonstrates how to isolate the absolute value term and set up two cases to find solutions. Suitable for students in Grades 8-10.

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