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 to complete this discussion:

According to the first letter of your last name, find the pair of compound inequalities assigned to you in the table below.

If the first letter of your last name is

Your “and” compound inequality is

Your “or” compound inequality is

A or L

-4 ≤ 3 + 7x < 24

5 – x ≥ 7 or 8x – 3 > 29

B or K

-16 ≤ 2 + 9x ≤ 11

12 – x > 15 or 4x – 13 > 7

C or J

-10 < -2 + 8x < 22

4x + 7 < 11 or 1 – x ≤ -2

D or I

-17 < 3 + 10x ≤ 33

5x + 3 ≤ -2 or 13 – x ≤ 6

E or H

-1 ≤ -3 + 2x < 17

7 – x ≥ 6 or 7x – 1 > 27

F or G

-12 < 12 + 4x < 0

12 – x > 15 or 7x – 13 > 1

M or Z

-1 ≤ 3 + 2x < 11

1 – x ≥ -3 or 5x – 1 > 19

N or Y

-1 < 4 + 5x ≤ 19

2x + 3 ≤ -1 or 10 – x ≤ 5

O or X

-4 ≤ 5 + 3x ≤ 11

2x + 2 < 2 or 3 – x ≤ 0

P or W

-9 < -1 + 4x < 15

8 – x > 15 or 6x – 13 > 11

Q or V

-10 < -3 + x ≤ 21

2 – x ≥ 1 or 6x – 1 > 17

R or U

-11 ≤ -5 + 6x < 13

3x + 2 ≤ -1 or 11 – x ≤ 4

S or T

0 ≤ 4 + 2x ≤ 22

3x + 6 < -3 or 5 – x ≤ 1

Solve the compound inequalities as demonstrated in Elementary and Intermediate Algebra and the Instructor Guidance in the left navigation toolbar, being 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 as demonstrated in the Instructor Guidance in the left navigation toolbar.

Incorporate the following five math vocabulary words into your discussion. Use bold font 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. Respond to at least two of your classmates’ posts by Day 7.

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