n 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. Please 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. 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.
- 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.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.

In this discussion, you will simplify and compare equivalent expressions written both in radical form and with rational (fractional) exponents. Read the following instructions in order and view the example to complete this discussion. Please find the rational exponent problems assigned to you in the table below:

If the last letter of your first name is |
On pages 576 – 577, do the following problems |

A or L | 42 and 101 |

B or K | 96 and 60 |

C or J | 46 and 104 |

D or I | 94 and 62 |

E or H | 52 and 102 |

F or G | 90 and 64 |

M or Z | 38 and 72 |

N or Y | 78 and 70 |

O or X | 44 and 74 |

P or W | 80 and 68 |

Q or V | 50 and 76 |

R or U | 84 and 66 |

S or T | 54 and 100 |

- Simplify each expression using the rules of exponents and examine the steps you are taking.
- 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 the thought behind your math work**.):- Principal root
- Product rule
- Quotient rule
- Reciprocal
*n*th root

Refer to Inserting Math Symbols for guidance with formatting. Be aware with regards to the square root symbol, you will notice that it only shows the front part of a radical and not the top bar. Thus, it is impossible to tell how much of an expression is included in the radical itself unless you use parenthesis. For example, if we have √12 + 9 it is not enough for us to know if the 9 is under the radical with the 12 or not. Therefore, we must specify whether we mean it to say √(12) + 9 or √(12 + 9), as there is a big difference between the two. This distinction is important in your notation.

Another solution is to type the letters “sqrt” in place of the radical and use parenthesis to indicate how much is included in the radical as described in the second method above. The example above would appear as either “sqrt(12) + 9” or “sqrt(12 + 9)” depending on what we needed it to say.

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.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.

In this discussion, you will solve quadratic equations by two main methods: factoring and using the quadratic formula. Read the following instructions in order and view the example to complete this discussion. Please find the problems assigned to you in the table below:

If the third letter of your last name is |
On pages 635 and 636, solve the following problem by factoring |
Solve the following problem by using the Quadratic Formula |

A or L |
46 |
48 on p. 646 |

B or K |
88 |
46 on p. 646 |

C or J |
84 | 44 on p. 646 |

D or I |
10 | 20 on p. 646 |

E or H |
8 | 18 on p. 646 |

F or G |
6 | 16 on p. 646 |

M or Z |
38 | 48 on p. 636 |

N or Y |
40 | 50 on p. 636 |

O or X |
42 | 52 on p. 636 |

P or W |
44 | 54 on p. 636 |

Q or V |
80 | 56 on p. 637 |

R or U |
2 | 78 on p. 637 |

S or T |
4 | 82 on p. 637 |

- For the factoring problem, be sure you show all steps to the factoring and solving. Show a check of your solutions back into the original equation.
- For the Quadratic Formula problem, be sure that you use readable notation while you are working the computational steps. Refer to the Inserting Math Symbols handout for guidance with formatting.
- Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.
- Incorporate the following four 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**.):- Quadratic formula
- Factoring
- Completing the square
- Discriminant

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.

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.

In this discussion, you will solve quadratic equations by two main methods: factoring and using the quadratic formula. Read the following instructions in order and view the example to complete this discussion. Please find the problems assigned to you in the table below:

If the third letter of your last name is |
On pages 635 and 636, solve the following problem by factoring |
Solve the following problem by using the Quadratic Formula |

A or L |
46 |
48 on p. 646 |

B or K |
88 |
46 on p. 646 |

C or J |
84 | 44 on p. 646 |

D or I |
10 | 20 on p. 646 |

E or H |
8 | 18 on p. 646 |

F or G |
6 | 16 on p. 646 |

M or Z |
38 | 48 on p. 636 |

N or Y |
40 | 50 on p. 636 |

O or X |
42 | 52 on p. 636 |

P or W |
44 | 54 on p. 636 |

Q or V |
80 | 56 on p. 637 |

R or U |
2 | 78 on p. 637 |

S or T |
4 | 82 on p. 637 |

- For the factoring problem, be sure you show all steps to the factoring and solving. Show a check of your solutions back into the original equation.
- For the Quadratic Formula problem, be sure that you use readable notation while you are working the computational steps. Refer to the Inserting Math Symbols handout for guidance with formatting.
- Present your final solutions as decimal approximations carried out to the third decimal place. Due to the nature of these solutions, no check is required.
- Incorporate the following four 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**.):- Quadratic formula
- Factoring
- Completing the square
- Discriminant

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.

In this discussion, you will be assigned two equations with which you will then do a variety of math work having to do with mathematical functions. Read the following instructions in order and view the example to complete this discussion. Please find the two equations assigned to you in the table below:

If the last letter of your last name is |
On pages 708 – 711, solve the following problems |

A or B | 22 and 30 |

C or D | 24 and 32 |

E or F | 26 and 34 |

G or H | 28 and 36 |

I or J | 12 and 46 |

K or L | 14 and 48 |

M or N | 16 and 50 |

O or P | 18 and 52 |

Q or R | 20 and 54 |

S or T | 2 and 56 |

U or V | 4 and 58 |

W or X | 6 and 60 |

Y or Z | 8 and 64 |

- First, graph your functions so you can clearly describe the graphs in your discussion. Your graph itself is not required in your post, although the discussion of the graph is required. Make sure you have at least five points for each equation to graph. Show all math work for finding the points.
- Mention any key points on the graphs, including intercepts, vertex, or start/end points. (Points with decimal values need not be listed, as they might be found in a square root function. Stick to integer value points.)
- Discuss the general shape and location of each of your graphs.
- State the domain and range for each of your equations. Write them in interval notation.
- State whether each of the equations is a function or not giving your reasons for the answer.
- Select one of your graphs and assume it has been shifted three units upward and four units to the left. Discuss how this transformation affects the equation by rewriting the equation to incorporate those numbers.
- 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 the thought behind your math work**.):- Function
- Relation
- Vertical Line test
- Transformation

Carefully review the Grading Rubric for the criteria that will be used to evaluate your discussion.

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