https://file.aiquickdraw.com/mathbot/file/1726283520473r3xs2v2j.jpg

The inequality you have uploaded is:

\[
|x| - 15 < -6
\]

To solve this inequality, follow these steps:

1. First, isolate the absolute value term by adding \(15\) to both sides:

\[
|x| < 9
\]

2. The general rule for an inequality involving an absolute value is:
   \[
   |x| < a \implies -a < x < a
   \]

   Applying this to the inequality \( |x| < 9 \), we get:

   \[
   -9 < x < 9
   \]

Thus, the solution to the inequality is \( -9 < x < 9 \).

Would you like further details or have any questions?

Here are 5 related questions:
1. What would the solution be if the inequality were \( |x| > 9 \)?
2. How would the inequality change if instead of \( -15 \), it was \( +15 \)?
3. What are the implications of having a negative number on the right-hand side of an absolute value inequality?
4. How does solving absolute value inequalities differ from equations without absolute values?
5. Can you graph the solution set of this inequality on a number line?

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

Learn how to solve the absolute value inequality |x| - 15 < -6 step by step. This problem involves isolating the absolute value term and applying key algebraic principles to find the solution. Suitable for students in Grades 8-10.

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