Solve the inequality |x^2 - 1| <= 0.

The inequality |x^2 - 1| <= 0 has only one solution, x = 1 or x = -1.

To solve this inequality, we first note that the absolute value of any real number is always non-negative. Therefore, |x^2 - 1| can only be less than or equal to zero if x^2 - 1 = 0. Solving for x, we get x = 1 or x = -1.

To verify that these are indeed solutions, we substitute them back into the original inequality. When x = 1, we have |1^2 - 1| = 0, which satisfies the inequality. Similarly, when x = -1, we have |-1^2 - 1| = 0, which also satisfies the inequality.

Therefore, the only solutions to the inequality |x^2 - 1| <= 0 are x = 1 and x = -1. We can represent this solution set using set-builder notation as {x | x = 1 or x = -1}.