Discussion 2

Week 2 – Discussion

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Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Carefully review the Grading Rubric for guidance on how your discussion will be evaluated.

One-Variable Compound Inequalities [CLOs: 1, 2]

In this discussion, you will be demonstrating your understanding of compound inequalities and the effect that dividing by a negative has on an inequality. Read the following instructions in order and view the example (available for download in your online classroom) to complete this discussion. Please complete the following problems according to your assigned number. (Instructors will assign each student their number.)

If your assigned number is:

Your “and” compound inequality is:

Your “or” compound inequality is:

1 –3 ≤ x + 2 < 9 7 + 2x < –1 or 13 – 5x ≤ 3
2 –1 ≤ x – 3 ≤ 5 –2x – 5 < –2 or x – 3 < –10
3 –10 < 3x – 1 < 5 6 > 2x – 1 or –4 ≤ –3x + 2
4 –18 < 4x + 2 ≤ 30 3x – 7 > –10 or 5x + 2 ≤ 22
5 4 ≤ x – 3 < 20 x + 3 < –2 or 3x – 4 < 8
6 –30 < 2x + 2 < 10 3x – 11 < 4 or 4x + 9 ≥ 1
7 –15 ≤ –4x –5 < 0 1 – x < –2 or 2x + 1 > 9
8 –5 < 4x + 1 ≤ 3 3x + 2 ≤ 2 or 3 – x ≤ 1
9 9 ≤ 5 + 2x ≤ 19 2x – 1 > 5 or 2 – 3x > 11
10 –2 < –1 – 4x < 12 2x – 7 ≤ 5 or 5 – 2x > 3
11 –3 < x + 5 ≤ 5 –3x – 5 > 4 or 4 – x ≤ 6
12 –28 ≤ 2 – 6x < 20 4x + 3 ≤ 16 or – 2x < 3
13 0 ≤ 4 + 2x ≤ 1 5 – 3x ≤ 8 or 2x + 1 > 7
14 10 ≤ 2 + 4x < 20 4x + 3 < 16 or –2x < 3
15 –12 ≤ 2 + 2x ≤ 10 2x – 1 ≥ 3 or x < –2
16 –6 < 3x – 9 ≤ 0 1 > 6x – 8 or 8x – 6 ≤ 10
17 –1 < 6x + 1 ≤ 13 5x –5 ≥ –5 or 5 – x ≤11
18 5 ≤ –3x – 2 < 8 5x ≤ 15 or –x – 6 < 1
19 –1 < –2x + 4 ≤ 5 x < 0 or 3x + 1 ≥ 7
20 0 ≤ 6x + 3 < 12 –x + 7 ≥ 10 or 3x – 3 ≤ 12
21 –2 < 26 + 7x ≤ 4 3x + 8 > 0 or – 2x ≥ 4
22 –7 < 2x – 5 ≤ –4 8x – 4 > 6 or 3x + 18 ≤ –6
23 –6 < 1 + 4x < 17 6x – 10 > 8 or 8x + 2 < 5
24 –2 < –4 + x ≤ 22 5x + 1 ≥ 6 or 2x – 5 ≤ –11
25 5 ≤ 5 + 4x < 13 6x + 2 ≤ –10 or 6x –12 ≥ 0
26 4 ≤ 2 + 4x ≤ 16 x + 2 < –1 or – x ≤ 9
27 0 ≤ –3 + 8x ≤ 22 2x – 9 ≤ 3 or 3x – 8 > 28
28 –4 ≤ 3 + 7x < 24 5 – x ≥ 7 or 8x – 3 > 29
29 –16 ≤ 2 + 9x ≤ 11 12 – x > 15 or 4x – 13 > 7
30 –10 < –2 + 8x < 22 4x + 7 < 11 or 1 – x ≤ –2
31 –17 < 3 + 10x ≤ 33 5x + 3 ≤ –2 or 13 – x ≤ 6
32 –1 ≤ –3 + 2x < 17 7 – x ≥ 6 or 7x – 1 > 27
33 –12 < 12 + 4x < 0 12 – x > 15 or 7x – 13 > 1
34 –1 ≤ 3 + 2x < 11 1 – x ≥ –3 or 5x – 1 > 19
35 –1 < 4 + 5x ≤ 19 2x + 3 ≤ –1 or 10 – x ≤ 5
36 –4 ≤ 5 + 3x ≤ 11 2x + 2 < 2 or 3 – x ≤ 0
37 –9 < –1 + 4x < 15 8 – x > 15 or 6x – 13 > 11
38 –10 < –3 + x ≤ 21 2 – x ≥ 1 or 6x – 1 > 17
39 –11 ≤ –5 + 6x < 13 3x + 2 ≤ –1 or 11 – x ≤ 4
40 0 ≤ 4 + 2x ≤ 22 3x + 6 < –3 or 5 – x ≤ 1
41 –3 ≤ x – 2 < 9 3x + 11 < 4 or 4x + 9 ≥ 1
42 –1 ≤ x + 3 ≤ 5 1 – x > –2 or 2x – 1 > 9
43 –10 < 3x + 1 < 5 3x – 2 ≤ 2 or 3 – x ≤ 1
44 –18 < 4x – 2 ≤ 30 2x + 1 < –5 or 2 + 3x > 11
45 4 ≤ x + 3 < 20 2x + 7 ≤ 5 or 7 – 2x < 3
  • Solve the compound inequalities as demonstrated in Elementary and Intermediate Algebra and the Instructor Guidance in the left navigation toolbar, in your online course. Be careful of how a negative x-term is handled in the solving process. Show all math work arriving at the solutions.
  • Show the solution sets written algebraically and as a union or intersection of intervals. Describe in words what the solution sets mean, and then display a simple line graph for each solution set. This is demonstrated in the Instructor Guidance in the left navigation toolbar, in your online course.
  • Incorporate the following five math vocabulary words into your discussion. Use boldfont to emphasize the words in your writing. Do not write definitions for the words; use them appropriately in sentences describing your math work.
    • Compound inequalities
    • And
    • Or
    • Intersection
    • Union

Your initial post should be at least 250 words in length. Support your claims with examples from required material(s) and/or other scholarly resources, and properly cite any references.