To solve the equation \( 26 = |x - 15| \), we need to break it down into two cases because the absolute value can result in either a positive or negative value.

### Case 1:
If \( x - 15 \geq 0 \), then \( |x - 15| = x - 15 \). So, the equation becomes:
\[
26 = x - 15
\]
Solving for \( x \):
\[
x = 26 + 15 = 41
\]

### Case 2:
If \( x - 15 < 0 \), then \( |x - 15| = -(x - 15) = 15 - x \). So, the equation becomes:
\[
26 = 15 - x
\]
Solving for \( x \):
\[
x = 15 - 26 = -11
\]

Thus, the solutions are:
\[
x = 41 \quad \text{or} \quad x = -11
\]

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How would you solve \( |x - a| = b \) in general?
2. What if \( 26 \) were a negative number in this absolute value equation?
3. Can you graph \( |x - 15| = 26 \) and explain the intersection points?
4. How would this problem change if the equation were \( 26 \leq |x - 15| \)?
5. What is the definition of an absolute value and how does it affect equations?

**Tip:** Always consider both the positive and negative cases when solving absolute value equations.

Explore how to solve the absolute value equation 26 = |x - 15| step by step, considering both the positive and negative cases. This problem is ideal for students learning algebra and absolute value concepts, suitable for Grades 7-9.

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