Absolute Value

[apple100]

1. 1 > |x^2|

2. 1 < |x^2|

3. 1 > |x|^2

4. 1 < |x|^2




How do you solve for x?

[Ian Stewart]

Since x^2 is never negative, x^2 = |x^2| = |x|^2. For each of the inequalities above, you can ignore the absolute value signs. So, for example, if |x|^2 < 1, that just means that -1 < x < 1.