HavenHub Math • Edition 9 • Unit 4

Workbook: The Comparison

The Scribe's Log of Boundaries and Territories

Lesson 4.1: The Boundary Symbols

Part 1: Reading the Alligator
1.Read this: $x > 10$.
[ ] x is greater than 10
[ ] x is less than 10
2.Read this: $n < 5$.
[ ] n is greater than 5
[ ] n is less than 5
3.Which symbol means "At Least"?
[ ] <     [ ] ≥     [ ] ≤
4.Which symbol means "No More Than"?
[ ] >     [ ] ≥     [ ] ≤
5.True or False: $5 ≤ 5$.
6.True or False: $5 < 5$.
7.Insert the correct symbol:
10 -2
8.Insert the correct symbol:
-100 -1

Lesson 4.2: Fences and Gates (Graphing)

The Territory Audit

1. Graph $x > 2$. (Use an open circle and shade right).

-5
0
5

2. Graph $x ≤ -1$. (Use a closed circle and shade left).

-5
0
5
Analysis
3.If the circle is Hollow, is the number included?
4.If the circle is Solid, is the number included?

Lesson 4.3: Maintaining the Relationship (Solving)

One-Step Inequalities
1.$x + 5 > 10$
Solution:
2.$n - 2 ≤ 8$
Solution:
3.$2y < 12$
Solution:
4.$x / 3 ≥ 4$
Solution:
5.$z + 100 < 100$
Solution:
6.$a - 15 > 5$
Solution:
7.$10x ≤ 50$
Solution:
8.$x / 10 < 2$
Solution:

Lesson 4.4: True or False (In Bounds)

Testing the Point
1.Rule: $x > 10$. Is 15 a solution?
2.Rule: $x < -5$. Is 0 a solution?
3.Rule: $x ≥ 0$. Is 0 a solution?
4.Rule: $x ≤ -10$. Is -20 a solution?
5.Rule: $2x > 10$. Is 6 a solution?
7.Rule: $x \ge -1$. Is -1 a solution?
8.Rule: $x < 0$. Is -100 a solution?
9.Rule: $|x| < 5$. Is -10 a solution?
10.Rule: $x/2 \ge 10$. Is 15 a solution?
11.Which is further from 0: -50 or 40?
12.Name a number that is greater than -10 but less than -5:
The Scribe's Discernment
13.Does an inequality have only one answer?
14.What is the "Minimum" of $x \ge 10$?
15.What is the "Maximum" of $x \le 50$?

Lesson 4.5: Real World Constraints

Translate the Rule
1."You must be over 4 feet tall to ride." (Use $h$):
2."The speed limit is 25 mph." (Use $s$):
3."Admission is free for those 5 and under." (Use $a$):
4."You must have at least 10 silver coins." (Use $c$):

Appendix A: The 100-Problem Density Block

Complete all 100 to earn the Watchman's Seal of the Wall.

1. $x > 1 o$ True
2. $x > 2 o$ True
3. $x > 5 o$ False if 4
4. $x > 10 o$ True if 11
5. $x < 0 o$ Negative
6. $x < -1 o$ colder than -1
7. $x ≥ 10 o$ 10 included
8. $x ≤ 10 o$ 10 included
9. $x > 10 o$ 10 excluded
10. $x < 10 o$ 10 excluded
11. $x + 1 > 5 o x > 4$
12. $x + 2 > 10 o x > 8$
13. $x - 1 < 10 o x < 11$
14. $x - 5 < 5 o x < 10$
15. $2x > 10 o x > 5$
16. $2x ≤ 20 o x ≤ 10$
17. $x/2 ≥ 5 o x ≥ 10$
18. $x/10 < 1 o x < 10$
19. $x+x > 10 o x > 5$
20. $3x ≥ 3 o x ≥ 1$
21. Inverse of $+$ is $-$
22. Inverse of $-$ is $+$
23. Inverse of $\times$ is $/$
24. Inverse of $/$ is $\times$
25. Boundary = Point
26. Shade Right = Greater
27. Shade Left = Lesser
28. Open = Fence
29. Closed = Gate
30. Flip Rule = Negative
31. $x + 0 > 5 o x > 5$
32. $x - 0 < 10 o x < 10$
33. $x × 1 ≥ 12 o x ≥ 12$
34. $x / 1 ≤ 15 o x ≤ 15$
35. $x × 0 < 1$ (Always)
36. $x + 10 ≥ 11 o x ≥ 1$
37. $x - 10 ≤ 0 o x ≤ 10$
38. $10x > 10 o x > 1$
39. $x / 10 < 1 o x < 10$
40. $x + 9 ≤ 10 o x ≤ 1$
41. 2-sided add
42. 2-sided sub
43. 2-sided mul
44. 2-sided div
45. Territory act
46. Verification test
47. Restoration act
48. Alignment act
49. Equilibrium act
50. Integrity act
51. $x + 7 > 14 o x > 7$
52. $x - 7 < 7 o x < 14$
53. $7x ≥ 49 o x ≥ 7$
54. $x / 7 ≤ 7 o x ≤ 49$
55. $x + 7 e 7 o x e 0$
56. $x + 15 > 20 o x > 5$
57. $x - 15 < 5 o x < 20$
58. $4x ≥ 40 o x ≥ 10$
59. $x / 4 ≤ 10 o x ≤ 40$
60. $x + 100 > 200 o x > 100$
61. If $x=1, x+1 > 1$
62. If $x=5, 2x ≥ 10$
63. If $x=10, x/2 < 10$
64. If $x=0, x+10 ≤ 10$
65. If $x=100, x-1 > 90$
66. Limit $x+1 > 2$
67. Limit $x-1 < 0$
68. Limit $2x ≥ 2$
69. Limit $x/2 ≤ 1$
70. Limit $x e x$ (Empty!)
71. Test $1+1 > 1$
72. Test $5-2 < 10$
73. Test $3 × 3 ≥ 9$
74. Test $10/2 ≤ 5$
75. Test $0+0 e 1$
76. Solve for the fence
77. Solve for the field
78. Solve for the budget
79. Solve for the speed
80. Solve for the soul
81. 1 is the Identity
82. 0 is the Identity
83. $x$ is the Discernment
84. $>$ is the Authority
85. $<$ is the Submission
86. $≥$ is the Mercy
87. $≤$ is the Stewardship
88. $≠$ is the Choice
89. Range is the Goal
90. Path is the Rule
91. $x$ + Debt < Zero
92. $n$ - Gain > Whole
93. $y ×$ Inverse = Ident
94. $z /$ Portion = Part
95. The Fence is Solid
96. The Gate is Clear
97. The Scribe is True
98. The King is Greater
99. The Kingdom is Wide
100. 1.00 Shalom

Instructions for the Scribe: Continue this pattern until you reach 100. Practice solving one-step inequalities and identifying solution sets on the number line. Accuracy is your Honor.

Appendix D: The Scribe's Constraint Project

Use this page to practice the art of defining the safe territory of the Kingdom.

Step 1: The Rule. Write an inequality for this constraint: "A traveler must carry less than 15 pounds of luggage."
Variable: $w$ (weight). Inequality:

Step 2: The Graph. Draw the number line representation of the luggage rule. Use the correct circle type!

Step 3: The Solve. A family has 3 bags. Each bag weighs $x$ pounds. The total weight must be at most 30 pounds.
$3x \le 30$. Solve for $x$:

Step 4: The Comparison. Is -10 a solution for $x < -2$?
[ ] Yes
[ ] No. Explain why using distance from the sun:

Appendix B: The Master's Final Audit

Check the boxes only when you have mastered the skill.

Certified by the Mentor

Appendix C: The Litany of the Boundary

Recite this to close the unit.

Mentor: Scribe, where is the safe land?

Student: Inside the boundary. Within the limit of the King's decree.

Mentor: Is the gate always closed?

Student: No. It is open for the greater, and closed for the exact, as the Scribe marks the line.

Mentor: What do we seek in the comparison?

Student: Discernment. Protection. The territory of truth.

Mentor: Go now, and walk within the infinite range of God's grace.

Student: Amen. Greater is He, and true is the path.

Unit 4 Complete!

You are ready for the Master Plan.

HALLELUYAH!