https://file.aiquickdraw.com/mathbot/file/1727210433953to3j2c1r.jpg

The equation shown is:

\[
|x - 1| + 5 = 2
\]

Let's solve this step by step.

### Step 1: Isolate the absolute value term
Subtract 5 from both sides:

\[
|x - 1| = 2 - 5
\]

\[
|x - 1| = -3
\]

### Step 2: Analyze the absolute value
The absolute value of any expression is always non-negative, meaning \(|x - 1| \geq 0\). Since \(|x - 1| = -3\) leads to a negative result, this equation has **no solution**.

Thus, there is no real value of \(x\) that satisfies this equation.

Would you like further explanation or details on this? 

Here are some related questions for practice:
1. How do you solve equations with absolute values?
2. What is the geometric meaning of absolute value on a number line?
3. How do you solve \(|x - 2| = 4\)?
4. Can absolute value ever be negative?
5. How does adding a constant outside an absolute value affect the solution?

**Tip**: Always check if the isolated absolute value equals a non-negative number; if not, there is no solution.

Learn how to solve the absolute value equation |x - 1| + 5 = 2 with a step-by-step solution. This problem focuses on isolating the absolute value term and analyzing possible solutions. Suitable for Grades 7-10, ideal for understanding absolute value concepts in algebra.

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