Download Algebra II Prep – Solving Absolute Value Equations

Algebra II Prep – Solving Absolute Value Equations (Notes)
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Essential Question
Standard(s):
A-REI- Represent and solve equations and inequalities graphically
11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values, or find successive approximations. Include cases
where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic
functions.
Key Concepts
Notes
ABSOLUTE VALUE EQUATIONS
There are three types of open
sentences that can involve absolute
value:
1.
2.
3.
Consider the first type, |x|=n. If
|x|=5 , what would this mean for the
value of x?
When solving equations that involve
absolute value, there are two cases to
consider:
CASE 1 –
CASE 2 –
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Consider the second type of open
sentences. If |x| < n , this is a
compound sentence that uses AND
CASE 1 –
CASE 2 –
Consider the second type of open
sentences. If |x| > n , this is a
compound sentence that uses OR
CASE 1 –
CASE 2 –
Equations involving absolute value can
be solved by graphing them on a
number line or by writing them as a
compound sentence and solving it!!
Summarize the three rules you
should remember when solving
equations and inequalities involving
absolute value.
1. If |x| = n, then
2. If |x| < n, then
3. If |x| > n, then
What if you replace > with > or < with
<?
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Example 1 – Solve an Absolute Value
Equation/Inequality – Level 1
a) a  4  3
b) 2 x  8  6
c) t  5  9
d) y  3  1
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Example 2 – Solve an Absolute Value
Equation/Inequality – Level 2
a) 8  (w  1)  9
b)
2  3x
2
5
c)
5h  2
7
6
d)
2
x  4  8
3
Summary, Reflection, & Analysis
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Attempts:
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Algebra II Prep – Solving Absolute Value Equations – LEVEL 1
Solve each equation or inequality. Must show all work!!!
1.
x 5  8
4.
w6  3
2.
b9  2
5.
z2 5
3.
n 3 1
6.
t 8  2
Attempts:
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Algebra II Prep – Solving Absolute Value Equations – LEVEL 2
Solve each equation or inequality. Must show all work!!!
7. 5c  8  12
10. 7  3 p  2
8.
3k  4  8
9.
6  (3d  5)  14
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11.
f 5
 3
3
12.
3
x3  6
4
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Attempts:
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Algebra II Prep – Solving Absolute Value Equations – LEVEL 3
Solve each equation or inequality. Must show all work!!!
13.
2x  6
4
4
14.
2
g4 2
3
15. 7r  9  2
16. 3 x  4  9
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Algebra II Prep – Solving Absolute Value Equations
CRITICAL THINKING ACTIVITY #1
1.
2. What does the symbol ± mean?
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a.
If x = 3 ± 1.2, what are the values of x?
b.
Write x = 3 ± 1.2 as an expression involving absolute value.
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