Post on 26-Mar-2015
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