The inequality given is \( |x + 1| < 4 \).

To solve this absolute value inequality, follow these steps:

### Step 1: Rewrite the inequality as a compound inequality
The expression \( |x + 1| < 4 \) implies:
\[
-4 < x + 1 < 4
\]

### Step 2: Solve for \( x \)
Now, subtract 1 from all parts of the inequality:
\[
-4 - 1 < x + 1 - 1 < 4 - 1
\]
\[
-5 < x < 3
\]

### Final solution:
The solution is:
\[
x \in (-5, 3)
\]

This means that \( x \) can take any value between -5 and 3, but not including -5 or 3.

Would you like more details, or have any questions?

Here are 5 related questions you might explore:
1. How do we solve \( |2x - 5| \leq 7 \)?
2. What is the solution to \( |x - 3| > 2 \)?
3. How do you graph the solution \( |x + 1| < 4 \)?
4. Can you explain the difference between \( |x + 1| < 4 \) and \( |x + 1| \leq 4 \)?
5. How do we solve absolute value inequalities with a greater than condition, like \( |x - 1| > 3 \)?

**Tip:** Always remember to interpret absolute value inequalities as two cases (one positive and one negative) before solving them!

Learn how to solve the absolute value inequality |x + 1| < 4 with a step-by-step solution. This covers key algebraic concepts, including absolute value inequalities and the compound inequality approach. Suitable for students in Grades 8-10.

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