https://file.aiquickdraw.com/mathbot/file/1726229719261j8l9au3v.jpg

The equation provided in the image is:

\[
|x - 1| = 4
\]

To solve this absolute value equation, we can break it into two cases:

1. **Positive case**: \( x - 1 = 4 \)
   - Solving for \(x\): 
   \[
   x = 4 + 1 = 5
   \]

2. **Negative case**: \( x - 1 = -4 \)
   - Solving for \(x\):
   \[
   x = -4 + 1 = -3
   \]

Therefore, the solutions for \( x \) are:
\[
x = 5 \quad \text{or} \quad x = -3
\]

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

Here are some related questions:

1. What are the general steps to solve an absolute value equation?
2. How would the solution change if the equation were \( |x - 1| \leq 4 \)?
3. How do you graph the solution \( |x - 1| = 4 \) on a number line?
4. What would happen if the absolute value equation was set equal to a negative number?
5. How does this method extend to more complex absolute value equations?

**Tip:** When solving absolute value equations, always consider both the positive and negative cases of the expression inside the absolute value.

Learn how to solve the absolute value equation |x - 1| = 4 with step-by-step breakdowns. This problem explores absolute value properties and involves solving two linear equations. Perfect for students in Grades 8-10.

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