To solve the inequality \(|x| > -1\), we need to consider the properties of absolute values and inequalities.

### Step 1: Understand the inequality

The absolute value \(|x|\) represents the distance of \(x\) from 0 on the number line. By definition:

\[
|x| \geq 0
\]

This means that \(|x|\) is always non-negative. The smallest value \(|x|\) can take is 0 (when \(x = 0\)).

### Step 2: Analyze the inequality

The inequality is \(|x| > -1\). Since \(|x|\) is always non-negative and \(-1\) is negative, \(|x|\) will always be greater than \(-1\) for any real number \(x\).

### Conclusion:

Since \(|x|\) is always greater than \(-1\) for any real number \(x\), the solution is:

\[
\boxed{\text{All real numbers} \ x \in \mathbb{R}}
\]

This means every real number satisfies the inequality \(|x| > -1\).

Would you like details on this explanation?

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Here are five related questions:

1. What if the inequality were \(|x| \geq 0\) instead of \(|x| > -1\)?
2. How would the solution change if the inequality were \(|x| > 1\) instead of \(|x| > -1\)?
3. What are the implications if the inequality was \(|x| < 1\) instead?
4. How would the solution change if the inequality were \(|x| \geq 2\)?
5. What is the effect of changing the sign inside the absolute value, such as \(|-x| > -1\)?

**Tip:** Remember that the absolute value of any real number is always non-negative, so inequalities involving absolute values often have different properties from regular linear inequalities.

Learn how to solve the inequality |x| > -1 with a detailed step-by-step explanation. Understand the properties of absolute values and inequalities in mathematics. Suitable for students in Grades 7-9.

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