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

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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.

Day 1 10/5/23

Absolute Value

Question 1
1.

Vocabulary Review: Mark each statement as True or False.

  • False
  • True
  • 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 17
17.
Solve this absolute Value equation:




+ Case
_______
- Case
_______


Question 18
18.
Solve this absolute Value equation:
+ Case
_______
- Case
_______


Question 19
19.
Solve this absolute Value equation:

+ Case
_______
- Case
_______


Day 2 10/2/24

Absolute Value Special Cases

Question 20
20.

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

Question 21
21.

Explain why this is not possible:

|x|= - 6

Question 22
22.
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 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:

-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 25
25.
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 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")
_______


Solving Inequalities

Essential Question: How do you solve and graph inequalities?


Learning Target: Students will be able to solve solve and graph inequalities that represent real-world problems.


Complete the entire assignment and show work for full credit. Responses with no work shown will receive no credit.

Question 27
27.

Solve and graph the inequality for the given variable.

Question 28
28.

Solve and graph the inequality for the given variable.

Question 29
29.

Solve and graph the inequality for the given variable.

Question 30
30.

Solve and graph the inequality for the given variable.

Question 31
31.

Solve and graph the inequality for the given variable.

Question 32
32.

Solve and graph the inequality for the given variable.

Question 33
33.

Solve and graph the inequality for the given variable.

Question 34
34.

Solve and graph the inequality for the given variable.

Day 3 10/3/24

Compound Inequalities

Question 35
35.

Complete these notes for compound inequalities.

Question 36
36.
Solve and graph the compound inequality for the given variable.



_______ or _______
Question 37
37.
Solve and graph the compound inequality for the given variable.



_______ or _______
Question 38
38.
Solve and graph the compound inequality for the given variable.



_______ or _______
Question 39
39.

Complete these notes for compound inequalities.

Question 40
40.
Solve and graph the compound inequality for the given variable.



_______ and _______
Question 41
41.
Solve and graph the compound inequality for the given variable.



_______ and _______
Question 42
42.
Solve and graph the compound inequality for the given variable.



_______ and _______
Question 43
43.
Solve and graph the compound inequality for the given variable.



_______ and _______

Day 4 10/4/24

Spiral Review

Come on you know you forgot this stuff already.



Prove me wrong...

Question 44
44.

Simplify this expression. Your answer should not have negative exponents.


Question 45
45.

Simplify this expression. Your answer should not have negative exponents.


Question 46
46.

Simplify this expression. Your answer should not have negative exponents.


Question 47
47.

Simplify this expression. Your answer should not have negative exponents.


Question 48
48.

Simplify this expression. Your answer should not have negative exponents.


Question 49
49.

Find the Product of these polynomials.

Question 50
50.

Find the Product of these polynomials.

Question 51
51.

Find the difference between these polynomials. (subtract them)

Question 52
52.

Find the Product

Question 53
53.

Find the Product:

Question 54
54.

Find the square of this binomial.

Question 55
55.

Find the square of this binomial.

Question 56
56.

Find the Product

Question 57
57.

Match the exponents and radical to their matching expressions

Draggable itemarrow_right_altCorresponding Item
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Question 58
58.

Match the exponents and radical to their matching expressions

Draggable itemarrow_right_altCorresponding Item
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Question 59
59.

Find the perimeter of the following:

Question 60
60.

Find the area of the following:

Ya dun

Question 12
12.
Solve this absolute Value equation:

|x+4|= 7


+ Case
_______
- Case
_______


Question 13
13.
Solve this absolute Value equation:

|x-2|=5

+ Case
_______
- Case
_______


Question 14
14.
Solve this absolute Value equation:


+ Case
_______
- Case
_______


Question 15
15.
Solve this absolute Value equation:

+ Case
_______
- Case
_______


Question 16
16.
Solve this absolute Value equation:

+ Case
_______
- Case
_______