To solve the inequality \( |X - 20| < 5 \), we will break it down into two separate inequalities because the absolute value represents the distance from 20, which must be less than 5. This can be written as:

\[
-5 < X - 20 < 5
\]

Next, we'll solve this compound inequality by adding 20 to all parts:

\[
-5 + 20 < X < 5 + 20
\]

\[
15 < X < 25
\]

So, the solution is:

\[
15 < X < 25
\]

This means \( X \) lies between 15 and 25, exclusive.

Would you like further details on this, or do you have any other questions?

Here are some related questions to explore:
1. What happens when the inequality is \( |X - 20| \leq 5 \)?
2. How do we solve \( |X + 10| > 7 \)?
3. What is the general approach to solving absolute value inequalities?
4. How do absolute value equations differ from inequalities?
5. Can absolute value inequalities have no solution?

**Tip:** When solving absolute value inequalities, always remember to set up two cases (positive and negative) to handle the range of possible values.

Discover how to solve the absolute value inequality |X - 20| < 5 with a detailed explanation. This step-by-step guide covers the key algebraic concepts involved, including absolute value properties and inequality theorems. Perfect for students in Grades 8-10.

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