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. MY ASSIGNED NUMBER IS 35.

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 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.

 
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import java.util.Scanner;_x000D_
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public class BaseFour{_x000D_
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public static void main(String[] args){_x000D_
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Scanner scan = new Scanner(System.in);_x000D_
String input = “”;_x000D_
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// So long as the String input is NOT 1-60 in length,_x000D_
// Ask the user to enter a valid base-4 number up to 60 digits_x000D_
// Save the next line of user input to the variable “input”_x000D_
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// If the input string is NOT base-4, tell the user “Bad input!”_x000D_
// Otherwise, tell the user “You entered [numeric value of input]”_x000D_
// You can call the methods like so:_x000D_
// isBaseFour(input) This will give you a true or false value_x000D_
// baseFourValue(input) This will give you a long value_x000D_
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private static boolean isBaseFour(String input){_x000D_
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// Go over each character of input_x000D_
// If that single character is NOT ‘0’ or’1′ or ‘2’ or ‘3’, return false immediately_x000D_
// If you finish going through the characters, return true_x000D_
return true;_x000D_
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private static long baseFourValue(String input){_x000D_
long result;_x000D_
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// To start, the exponent is 0 and the next position in _x000D_
// in the input string is the string length minus one. _x000D_
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// Get the character at the next position in the input string_x000D_
// and store it in a char variable_x000D_
// Subtract ‘0’ (not 0) from that character and multiply _x000D_
// the result of that subtraction by (long) Math.pow(4, exponent)_x000D_
// When the loop is finished, assign the result to the variable “result”_x000D_
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return result;_x000D_
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You will need to do the following things:

Get a String of input from the user.
Depending on whether the input is valid, announce the number’s value; otherwise, let the user know it is bad input.
Write a method to verify whether or not the user’s input string is valid.
Write a method to calculate the value of the user’s input string.

 
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