We are given the inequality:

\[
2|x - 2| + 6 \geq 26
\]

### Step 1: Isolate the absolute value term.
Subtract 6 from both sides:

\[
2|x - 2| \geq 20
\]

### Step 2: Divide by 2.
\[
|x - 2| \geq 10
\]

### Step 3: Solve the absolute value inequality.
The absolute value inequality \(|x - 2| \geq 10\) means that:

\[
x - 2 \leq -10 \quad \text{or} \quad x - 2 \geq 10
\]

### Step 4: Solve each part.

1. \(x - 2 \leq -10\):
\[
x \leq -8
\]

2. \(x - 2 \geq 10\):
\[
x \geq 12
\]

### Final Solution:
The solution to the inequality is:

\[
x \leq -8 \quad \text{or} \quad x \geq 12
\]

In interval notation, this is:

\[
(-\infty, -8] \cup [12, \infty)
\]

Would you like further details or explanations?

Here are 5 related questions to expand your understanding:
1. How do you solve absolute value equations?
2. What is the difference between solving absolute value inequalities with "<" and ">”?
3. How can you graph the solution to an absolute value inequality?
4. What are the steps to solve compound inequalities?
5. How do you check if a value satisfies an absolute value inequality?

**Tip:** When solving absolute value inequalities, always remember that \(|a| \geq b\) means \(a \leq -b\) or \(a \geq b\).

Learn how to solve the absolute value inequality 2|x - 2| + 6 >= 26 with a detailed step-by-step solution. This problem covers essential algebraic concepts and the Absolute Value Inequality Theorem, suitable for students in Grades 9-11.

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