Lessons 1-4 & 1-6 Solving Absolute Value Equations & Inequalities ...
Lessons 14 & 16 Solving Absolute Value Equations & Inequalities.notebook January 30, 2015
Lessons 14 & 16
Solving Absolute Value Equations & Absolute Value Inequalities Lesson Objectives
Definition The Absolute Value of a number is its distance from 0 on the number line. Since distance is nonnegative, the absolute value of a number is always positive.
• Evaluate expressions involving absolute values
• Solve absolute value equations
Symbol:
5
4
3
2
1
0
1
2
3
4
5
• Solve absolute value inequalities
CCSS Addressed: A.CED.1 & A.SSE.1.b
Dec 2411:25 AM
Dec 292:16 PM
Solving Absolute Value Equations: Examples
Steps For Solving Absolute Value Equations 1.
Isolate the absolute value.
ALWAYS check your solutions! This is not to check for solving mistakes, it is to check for extraneous solutions!
2.
If the absolute value equals a positive number, write two separate equations without the absolute value signs.
ex)
3.
If the absolute value equals a negative number, there is no solution.
4.
If the absolute value equals zero, solve the equation and there is one solution.
5.
Solve each equation separately using the same steps as solving linear equations.
6.
CHECK ANY AND ALL SOLUTIONS!
case 1:
case 2:
ex)
case 1:
Feb 131:23 PM
case 2:
Dec 292:17 PM
Lesson 16: Solving Absolute Value Inequalities ex)
great"OR"
This has two solutions 5 and 5
Dec 292:20 PM
less th"AND"
Dec 292:21 PM
1
Lessons 14 & 16 Solving Absolute Value Equations & Inequalities.notebook January 30, 2015
ex) Solve
10
9
8
. Graph the solution set on the number line.
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
ex) Solve
. Graph the solution set on the number line.
10 10
9
8
7
6
5
4
3
Dec 292:21 PM
2
1
0
1
2
3
4
5
6
7
8
9
10
Sep 88:17 PM
Practice Problems ex) Solve
10
9
8
. Graph the solution set on the number line.
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
1)
2)
3)
4)
10
Sep 79:07 PM
Sep 79:10 PM
Writing Absolute Value Inequalities from a Graph
Writing Absolute Value Inequalities from a Graph ex)
ex) 10
9
8
7
6
5 4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
10
9
8
7
6
5 4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
10
9
8
7
6
5 4
3
2
1
0
2
1
9
8
7
6
5
4
3
10
ex)
ex)
Jan 2912:12 PM
10
9
8
7
6
5 4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Jan 2912:12 PM
2
Lessons 14 & 16 Solving Absolute Value Equations & Inequalities.notebook January 30, 2015
homework:
p. 30 #1432 even, 33 and
p. 45 # 1826
Dec 292:22 PM
3
Lessons 14 & 16
Solving Absolute Value Equations & Absolute Value Inequalities Lesson Objectives
Definition The Absolute Value of a number is its distance from 0 on the number line. Since distance is nonnegative, the absolute value of a number is always positive.
• Evaluate expressions involving absolute values
• Solve absolute value equations
Symbol:
5
4
3
2
1
0
1
2
3
4
5
• Solve absolute value inequalities
CCSS Addressed: A.CED.1 & A.SSE.1.b
Dec 2411:25 AM
Dec 292:16 PM
Solving Absolute Value Equations: Examples
Steps For Solving Absolute Value Equations 1.
Isolate the absolute value.
ALWAYS check your solutions! This is not to check for solving mistakes, it is to check for extraneous solutions!
2.
If the absolute value equals a positive number, write two separate equations without the absolute value signs.
ex)
3.
If the absolute value equals a negative number, there is no solution.
4.
If the absolute value equals zero, solve the equation and there is one solution.
5.
Solve each equation separately using the same steps as solving linear equations.
6.
CHECK ANY AND ALL SOLUTIONS!
case 1:
case 2:
ex)
case 1:
Feb 131:23 PM
case 2:
Dec 292:17 PM
Lesson 16: Solving Absolute Value Inequalities ex)
great"OR"
This has two solutions 5 and 5
Dec 292:20 PM
less th"AND"
Dec 292:21 PM
1
Lessons 14 & 16 Solving Absolute Value Equations & Inequalities.notebook January 30, 2015
ex) Solve
10
9
8
. Graph the solution set on the number line.
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
ex) Solve
. Graph the solution set on the number line.
10 10
9
8
7
6
5
4
3
Dec 292:21 PM
2
1
0
1
2
3
4
5
6
7
8
9
10
Sep 88:17 PM
Practice Problems ex) Solve
10
9
8
. Graph the solution set on the number line.
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
1)
2)
3)
4)
10
Sep 79:07 PM
Sep 79:10 PM
Writing Absolute Value Inequalities from a Graph
Writing Absolute Value Inequalities from a Graph ex)
ex) 10
9
8
7
6
5 4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
10
9
8
7
6
5 4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
10
9
8
7
6
5 4
3
2
1
0
2
1
9
8
7
6
5
4
3
10
ex)
ex)
Jan 2912:12 PM
10
9
8
7
6
5 4
3
2
1
0
1
2
3
4
5
6
7
8
9
10
Jan 2912:12 PM
2
Lessons 14 & 16 Solving Absolute Value Equations & Inequalities.notebook January 30, 2015
homework:
p. 30 #1432 even, 33 and
p. 45 # 1826
Dec 292:22 PM
3
