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Solve:  | x² - 1 |  < 1

Since this is an absolute value inequality, it can be written as:

      -1  <  x² - 1  < 1

Adding 1 to all three parts:

       0  <  x²  <  2

Since this is a squared inequality, take the square root; the values for x can be either positive or negative, so the final solution is:

     - sqrt(2)  <  x  <  0     or     0  <  x  <  sqrt(2)