Determine the value of x for which (x2 - 1) > 0

We want to solve the inequality (x² - 1) > 0 for x. To do this, we can factor the left-hand side of the inequality: (x² - 1) = (x - 1)(x + 1) Now we have the inequality: (x - 1)(x + 1) > 0 The product of two factors is positive if and only if both factors are positive or both factors are negative. So we can break the inequality into two cases: Case 1: (x - 1) > 0 and (x + 1) > 0 This simplifies to x > 1, which means x is greater than 1. Case 2: (x - 1) < 0 and (x + 1) < 0 This simplifies to x < -1, which means x is less than -1. Therefore, the solution to the inequality (x² - 1) > 0 is: x < -1 or x > 1 So the answer is: x < -1 or x > 1.