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2.4 absolute value equations(2) ink.notebook
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October 05, 2016
page 88
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2.4 Absolute
Value
Equations
Lesson Objectives
Standards
page 89
2.4 Solving Absolute Value Equations
Press the tabs to view details.
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2.4 absolute value equations(2) ink.notebook
Standards
Lesson Notes
A.REI.1 I will explain how to solve an absolute value equation A.REI.3 I will solve an absolute value equation Press the tabs to view details.
My Definition:
The distance a number
is from zero on the
number line.
3
= 3
-5 = 5
0
= 0
Lesson Objectives
Standards
Lesson Notes
A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Press the tabs to view details.
Characteristics:
Has absolute
value bars
"
appy bars "
Evaluate the expressions if n = 7 and t = 1. a)
b)
Is ALWAYS
positive or zero
Absolute Value
Example:
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Counterexample:
3
-3
opposite
1
3
3
1
reciprocal
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2.4 absolute value equations(2) ink.notebook
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When I want to determine something like, what I’m really asking myself is: What numbers are 4 units away from 0? Let’s look at a number line:
x + 0 = 4
What two numbers both have a distance of 4 away from 0? ________ and ________
To Solve Absolute Value Equations:
1) Make sure the absolute value
expression is isolated.
2) Set the "INSIDE" equation to
both positive and negative
number from the other side of
the equation. (Write 2 equations)
3) Solve BOTH equations.
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2.4 absolute value equations(2) ink.notebook
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Since distance is ALWAYS positive, the absolute
values of a number will NEVER be NEGATIVE!
= POSITIVE number
= POSITIVE number
= NEGATIVE number
= NEGATIVE number
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2.4 absolute value equations(2) ink.notebook
= POSITIVE number
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= NEGATIVE number
Solve each equation by showing all work. 1.
2.
Solve each equation by showing all work. 3.
4.
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2.4 absolute value equations(2) ink.notebook
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Solve each equation by showing all work. 5.
6.
Write an equation involving absolute value for each graph.
7.
8.
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2.4 absolute value equations(2) ink.notebook
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On Your
Whiteboards
a)
b)
On the
Worksheet
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2.4 absolute value equations(2) ink.notebook
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Evaluate each expression if r = –2, n = –3, and t = 3. 1.
Homework
Solve each equation by showing all work. Then graph the solution set. 4.
5.
2.
3.
6.
7.
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2.4 absolute value equations(2) ink.notebook
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8.
9.
10.
11.
12.
13.
14.
15.
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2.4 absolute value equations(2) ink.notebook
16.
17.
Write an equation involving absolute value for each graph.
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18.
Review. Simplify each radical by using perfect squares. Show your work!
20.
Perfect squares
19.
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
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2.4 absolute value equations(2) ink.notebook
Perfect squares
Review. Simplify each radical by using perfect squares. Show your work!
1
4
9
16
25
36
49
64
81
100
121
144
169
196
225
October 05, 2016
Answers:
1) –2 3) –2 5) a = –3, a = –1 7) x = –4, x = 4 9) x = –8, x = 2 11) n = –5.5, n = 5.5 13) x = –1, x = 8 15) x = –2.75, x = 6.25 17) no solution
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