Exercise 63 Page 47

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

Solution Set: x ≤ - 8.4 or x ≥ 9.6
Graph:

Practice makes perfect

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

1/9|5x-3|-3 ≥ 2

AddIneq

LHS+3≥RHS+3

1/9|5x-3| ≥ 5

MultIneq

LHS* 9 ≥ RHS * 9

|5x-3| ≥ 45

We are asked to find and graph the solution set for all possible values of x in the given inequality. |5x-3|≥ 45

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 or equal to 45 away from the midpoint in the positive direction or any number greater than or equal to 45 away from the midpoint in the negative direction. 5x-3 ≥ 45 or 5x-3 ≤ - 45 Let's isolate x in both of these cases before graphing the solution set.

Case 1

5x-3 ≥ 45

AddIneq

LHS+3≥RHS+3

5x ≥ 48

DivIneq

.LHS /5.≥.RHS /5.

x ≥48/5

CalcQuot

Calculate quotient

x≥ 9.6

This inequality tells us that all values greater than or equal to 9.6 will satisfy the inequality.

Case 2

5x-3 ≤ - 45

AddIneq

LHS+3≤RHS+3

5x ≤ - 42

DivIneq

.LHS /5.≤.RHS /5.

x ≤ -42/5

CalcQuot

Calculate quotient

x≤- 8.4

This inequality tells us that all values less than or equal to - 8.4 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 ≥ 9.6 Second Solution Set:& x ≤- 8.4 Combined Solution Set:& x ≤ - 8.4 or x ≥ 9.6

Graph

The graph of this inequality includes all values less than or equal to - 8.4 or greater than or equal to 9.6. We show this by keeping the endpoints closed.

Subchapter links

Lesson Check p.45

Practice and Problem-Solving Exercises p.46-48

Standardized Test Prep p.48

Mixed Review p.48

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Exercise 63 Page 47

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Case 1

Case 2

Solution Set

Graph