Exercise 66 Page 47

Create an or compound inequality because the absolute value is greater than or equal to the given value.

Solution Set: x<- 32orx>22
Graph:

Practice makes perfect

Before we can solve this inequality, we need to isolate the absolute value expression using the Addition Property of Inequality.

|x+5/3|-3>6

AddIneq

LHS+3>RHS+3

|x+5/3|>9

We are asked to find and graph the solution set for all possible values of x in the given inequality. |x+5/3|> 9

To do this, we will create a compound inequality by removing the absolute value. In this case, the solution set is any number greater than 9 away from the midpoint in the positive direction or any number greater than 9 away from the midpoint in the negative direction. x+5/3 > 9 or x+5/3 < - 9 Let's isolate x in both of these cases before graphing the solution set.

Case 1

x+5/3 > 9

MultIneq

LHS* 3 > RHS * 3

x+5 > 27

SubIneq

LHS-5>RHS-5

x > 22

This inequality tells us that all values greater than 22 will satisfy the inequality.

Case 2

x+5/3 < - 9

MultIneq

LHS* 3 < RHS * 3

x+5 < -27

SubIneq

LHS-5

x < - 32

This inequality tells us that all values less than -32 will satisfy the inequality.

Solution Set

The solution to this type of compound inequality is the combination of the solution sets. First Solution Set:& x >22 Second Solution Set:& x < -32 Combined Solution Set:& x < -32 or x > 22