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1.4 Solving Absolute Inequalities (Due 10/18/24)

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Last updated 15 days ago
24 questions
Required
20
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20
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20
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20
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20
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10
A.CED.1
A.SSE.1.b
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10
A.CED.1
A.SSE.1.b
Required
2
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2
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2
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2
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5
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5
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5
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5
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12
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12
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12
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8
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20
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20
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20
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20
Essential Question:How can we solve and interpret absolute value inequalities to find the range of possible solutions?

Learning Target: Students will be able to solve absolute value inequalities and represent their solutions on a number line, understanding how the inequality affects the direction and type of solution set (e.g., union of intervals or a bounded interval).

Show your work for credit.

Day 1 10/21/24

Question 1
1.
Solve, graph, and write the solutions to the following inequalities in interval notation.


_______ U_______
Question 2
2.

Solve, graph, and write the solutions to the following inequalities in interval notation.

Question 3
3.
Solve, graph, and write the solutions to the following inequalities in interval notation.

_______U_______
Question 4
4.

Solve, graph, and write the solutions to the following inequalities in interval notation.

Question 5
5.

Solve, graph, and write the solutions to the following inequalities in interval notation.

Spiral Review

Question 6
6.

Reasoning: Explain why the absolute value equation |3x| + 8 = 5 has no solution.

Question 7
7.
Compare and Contrast: Explain the similarities and differences in solving these inequalities |x - 1| ≤ 2 and |x - 1| ≥ 2.

Compare these two inequalities. (How are they alike?)
_______

Contrast these two inequalities. (How are they different?)
_______
Question 8
8.

Is this an open or closed interval?

Question 9
9.

Is this an open or closed interval?

Question 10
10.

Is this an open or closed interval?

Question 11
11.

Is this an open or closed interval?

Question 12
12.

Use interval notation to describe the range of this function.

Question 13
13.

Use interval notation to describe the domain of this function.

Question 14
14.

Write the following in interval notation.

Question 15
15.

Write the following in interval notatin.

Question 16
16.

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

  • |x|<2
  • -2<x<2
Question 17
17.

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

  • -3≤x≤13
  • |x|<4
Question 18
18.

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

  • |x-2.5|<1.5
  • x<3 or x>5
Question 19
19.

Match each inequality, absolute value, and interval notation with the correct graph. (Not every choice will be used)

  • (5,9]
  • (-∞,5)∪[9,∞)
  • 5<x≤9
  • x≤5 or x>9

Day 2 10/22/25

More Solving Absolute Value Inequalities

Question 20
20.

Solve and graph the inequality


Question 21
21.

Solve and graph the inequality:

Question 22
22.

Solve and graph the inequality:

Question 23
23.

Solve and graph.

Question 24
24.

Solve and graph the inequality:

-2≤x≤2
|x|>2
|x|≤2
x<-2 or x>2
(-2,2)
|x|≥2
(-∞,-2)∪(2,∞)
(-3,13)
|x-5|<8
|x|>4
x≤-4 or x≥4
[-3,13]
x<-4 or x>4
(-∞,-4)∪(4,∞)
(-∞,3)∪(5,∞)
x<1 or x≥4
1>x≤4
1<x≤4
3<x<5
(1,4]
|x-4|>1
x<5 or x≥9
(-∞,5]∪(9,∞)
(5,9)