Lesson 2-4 Absolute value in open sentenceAbsolute value in open sentenceAbsolute value in open sentenceAbsolute value in open sentence

Case1:Case1:Case1:Case1: |x| = a

Case2:Case2:Case2:Case2: |x| < a

Case3:Case3:Case3:Case3: |x| > a

Objective:Objective:Objective:Objective: Solving absolute value inequalitySolving absolute value inequalitySolving absolute value inequalitySolving absolute value inequality

Absolute Value of a number is …

Lesson 2-4 Definition of Absolute valueDefinition of Absolute valueDefinition of Absolute valueDefinition of Absolute value

The distance of that number from zero.

|-3| Read as “The distance of -3 from zero ”

|-3 | =3

|+5| Read as “The distance of +5 from zero ”

|+5 | =5

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 -3

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 5

Lesson 2-4 Case1:Case1:Case1:Case1:

Solve and graph

|x| = a

|x| = 7

x = 7 x = -7OR

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 7-7

Graph

Lesson 2-4 ExampleExampleExampleExample

Solve and graph |x + 4| = 5

x + 4 = 5 x + 4 = -5OR -4 -4 -4 -4

x = 1 x = -9

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7-8-9 1-9

Graph

Lesson 2-4 ExampleExampleExampleExample

Solve and graph |2x - 3| - 11 = - 4

Before start solving,

you MUST ISOLATE the

absolute value expression

on one side

|2x - 3| - 11 = - 4 +11 +11

|2x - 3| = 7

2x - 3 = 7 2x - 3 = -7OR +3 +3 +3 +3

2x = 10 2x = - 42 2

x = 5

2 2

x = -2

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7-8-9 -2 5

Lesson 2-4 Case2:Case2:Case2:Case2: |x| < a

Solve and graph |x| < 6

-6 < x < 6

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 6-6

Graph

Lesson 2-4 ExampleExampleExampleExample

Solve and graph |x + 4| ≤ 2

-2 ≤ x + 4 ≤ 2

Graph

-4 -4 -4

-6 ≤ x ≤ -2

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 -2-6

Lesson 2-4 ExampleExampleExampleExample

Solve and graph |x - 1| -5 < - 4

-1 < x – 1 < 1 +1 +1 +1

0 < x < 2

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 20

Before start solving,

you MUST ISOLATE the

absolute value expression

on one side

|x - 1| -5 < - 4 +5 +5

|x - 1| < 1

Lesson 2-4 Case2:Case2:Case2:Case2: |x| > a

Solve and graph |x| > 2

x > 6

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 6-6

Graph

x < - 6OR

Lesson 2-4 ExampleExampleExampleExample

Solve and graph |x – 3| ≥ 1

x – 3 ≥ 1

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 42

Graph

x – 3 ≤ - 1OR

+3 +3

x ≥ 4

+3 +3

x ≤ 2

Lesson 2-4 ExampleExampleExampleExample

Solve and graph |x + 3| + 2 > 5

Before start solving,

you MUST ISOLATE the

absolute value expression

on one side

|x + 3| + 2 > 5 -2 -2

|x + 3| > 3

x + 3 > 3

0 1 2 3 4 5 6 7-1-2-3-4-5-6-7 0-6

x + 3 < - 3OR

-3 -3

x > 0

-3 -3

x < -6