The inequality $x^2 \leq 1$ can be solved as follows:

1. Start by recognizing that $x^2 \leq 1$ can be rewritten as: $-1 \leq x \leq 1$ This inequality holds because the square of any number between -1 and 1 (inclusive) will be less than or equal to 1.

2. Therefore, the solution to $x^2 \leq 1$ is the interval: $x \in [-1, 1]$

In interval notation, the solution is $[-1, 1]$.

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Here are five related questions to expand on this concept:

1. How would the solution change for the inequality $x^2 < 1$?
2. What is the solution to $x^2 \geq 1$?
3. How would you solve $x^2 \leq 4$ instead of 1?
4. How do you solve an inequality with an absolute value, like $|x| \leq 2$?
5. What happens when solving $x^4 \leq 1$ instead of $x^2$?

Tip: When solving inequalities involving squares, always consider how the square of a number behaves over both negative and positive ranges.