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1.3 Solving Absolute Value Equations (Due 10/4/24)

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Last updated 15 days ago
31 questions
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Learning Target: How can we solve absolute value equations, and what do the solutions represent in different contexts? Essential Question: Students will be able to solve absolute value equations and identify when they result in one solution, two solutions, or no solution, and represent these solutions on a number line.


Show your work for credit.

Absolute Value

Question 1
1.

Vocabulary Review: Mark each statement as True or False.

  • True
  • False
  • To indicate the absolute value of -8, you write |-8|.
  • The absolute value of -8 is -8, since -8 is 8 units from 0 on the number line.
  • The absolute value of -8 is 8, since -8 is 8 units from 0 on the number line.
  • According to the definition of absolute value, if |r|= 3, then r = 3 or r = -3.
Question 2
2.

The definition of absolute value is...

Question 3
3.

Find the absolute value of this expression:

Question 4
4.

Find the absolute value of this expression:

Question 5
5.

Find the absolute value of this expression:

Question 6
6.

Find the absolute value of this expression:

Question 7
7.

Find the absolute value of this expression:

Question 8
8.

Find the absolute value of this expression:

Question 9
9.

Find the absolute value of this expression:

Question 10
10.

Question 11
11.

Find the absolute value of this expression:

Solving Absolute Value Equations

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Question 18
18.
Solve this absolute Value equation:




+ Case
_______
- Case
_______

Write your answer in set notation
x=_______
Question 19
19.
Solve this absolute Value equation:
+ Case
_______
- Case
_______

Write your answer in set notation
h=_______
Question 20
20.
Solve this absolute Value equation:

+ Case
_______
- Case
_______

Write your answer in set notation
n=_______

Day 2 10/2/24

Absolute Value Special Cases

Question 21
21.

In math, is there a difference between distance and direction?

Question 22
22.

Explain why this is not possible:

|x|= - 6

Question 23
23.
Solve this absolute Value equation:

-3|2x+1|=21


Does this have a solution?
_______

+ Case (If no solution exists, then write "no solution")
_______
- Case (If no solution exists, then write "no solution")
_______
Question 24
24.
Solve this absolute Value equation:

-3|2x+1|=-21


Does this have a solution?
_______

+ Case (If no solution exists, then write "no solution")
_______
- Case (If no solution exists, then write "no solution")
_______
Question 25
25.
Solve this absolute Value equation:

-5|4x-3|=-45


Does this have a solution?
_______

+ Case (If no solution exists, then write "no solution")
_______
- Case (If no solution exists, then write "no solution")
_______
Question 26
26.
Solve this absolute Value equation:

|3b+9|-16=-45


Does this have a solution?
_______

+ Case (If no solution exists, then write "no solution")
_______
- Case (If no solution exists, then write "no solution")
_______
Question 27
27.
Solve this absolute Value equation:

-|3b+9|-16=-45


Does this have a solution?
_______

+ Case (If no solution exists, then write "no solution")
_______
- Case (If no solution exists, then write "no solution")
_______

Learning Log

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Question 28
28.

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Question 29
29.

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Question 30
30.

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Question 12
12.
What are the 4 steps to solve an Absolute Value Equations?
1._______
2._______
3._______
4._______
Question 13
13.
Solve this absolute Value equation:

|x+4|= 7


+ Case
_______
- Case
_______

Write your answer in set notation
x=_______
Question 14
14.
Solve this absolute Value equation:

|x-2|=5

+ Case
_______
- Case
_______

Write your answer in set notation
x=_______
Question 15
15.
Solve this absolute Value equation:


+ Case
_______
- Case
_______

Write your answer in set notation
n=_______
Question 16
16.
Solve this absolute Value equation:

+ Case
_______
- Case
_______

Write your answer in set notation
c=_______
Question 17
17.
Solve this absolute Value equation:

+ Case
_______
- Case
_______

Write your answer in set notation
z=_______
Question 31
31.