Help with Algebra I...................?

to say the absolute value of a number is less than a positive number k, means that it is closer to zero than k is. all the positive (and negative) real numbers closer to zero than k is, is a connected set-you can conjoin the negative ones and the positive ones together by zero, making one long strip of numbers. if |x|>k, the numbers farther from zero than k is, have a "hole" in the middle (namely the strip described by the first conjunction). that is why you need 2 statements: one for the numbers further and left from zero than k (these are the negative ones), and one for the numbers further from zero than k is, and to the right of zero (positive).