Exercise 57 Page 211

To solve the inequality for the all possible values of n, we first need to isolate the absolute value. Remember that when you multiply or divide an inequality by a negative number, the inequality changes directions.

|n|-5/4<5

AddIneq

LHS+5/4

|n|<5+5/4

AddTerms

Add terms

|n|<6 14

Now that we have isolated the absolute value, we need to remove the absolute value. In this case, the solution set is any number less than 6 14 away from the midpoint in the positive direction and any number less than 6 14 away from the midpoint in the negative direction. Absolute Value Inequality:& |n| < 6 14 Compound Inequality:& -6 14 < n < 6 14 This compound inequality means that the distance between n and 0 is greater than -6 14 and less than 6 14.