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 \( [-1, 1] \).

Would you like further explanation or details on this?

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.

Learn how to solve the inequality x² ≤ 1 with a step-by-step solution. This problem explores key algebraic concepts, including solving inequalities and understanding the properties of quadratic functions. Suitable for students in Grades 9-10.

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