Exercise 25 Page 91

In order to rewrite this sentence into an absolute value inequality, we should first remember the standard form for an absolute value equation. |x-Midpoint|=Distance Let n be our variable. We can fill in the numerical information. & Half of a number... 5units from14 & | 1/2n- 14|... 5Since we need the distance from 14 to be at most 5 units, we will use ≤. & Half of a number... 5units from14 & | 1/2n- 14|≤ 5 Now we can solve this inequality by splitting the absolute value into two cases. Because we want the distance to be at most 5, we will need to write an and inequality. 1/2n-14 ≤ 5 and 1/2n-14 ≥ - 5 We can solve these cases separately and then combine the results. We will begin with the first case.

1/2n-14 ≤ 5

AddIneq

LHS+14≤RHS+14

1/2n ≤ 19

MultIneq

LHS* 2 ≤ RHS * 2

n≤38

Let's solve the second case.

1/2n-14 ≥ - 5

AddIneq

LHS+14≤RHS+14

1/2n ≥ 9

MultIneq

LHS* 2 ≥ RHS * 2

n≥18

With this information we can write the solution set for this compound inequality. n≤38 and n≥18 This is the set of all numbers between 18 and 38. 18 ≤ n ≤ 38