Inequalities on a Number Line Worksheet | Printable PDF Worksheets - Free Printable

I'll solve this worksheet step by step, working through each section carefully.

## Section A: Writing inequalities from number lines

Let me analyze each number line:

Row 1:
1. Open circle at -1, arrow to the right → x > -1
2. Open circle at -1, arrow to the left → x < -1
3. Open circle at 0, arrow to the right → x > 0

Row 2:
4. Closed circle at 1, arrow to the right → x ≥ 1
5. Closed circle at -2, arrow to the right → x ≥ -2
6. Closed circle at -2, arrow to the left → x ≤ -2

Row 3:
7. Open circles at -1 and 3, line between them → -1 < x < 3
8. Closed circles at -2 and 1, line between them → -2 ≤ x ≤ 1
9. Open circle at -2, closed circle at 1, line between them → -2 < x ≤ 1

## Section B: Illustrating inequalities on number lines

For each inequality, I need to determine:
- Whether to use open or closed circles (open for < or >, closed for ≤ or ≥)
- Which direction to shade

1. x ≤ -3: Closed circle at -3, shade to the left
2. x > 1: Open circle at 1, shade to the right
3. x ≥ -5: Closed circle at -5, shade to the right
4. -5 ≤ x < 7.5: Closed circle at -5, open circle at 7.5, shade between
5. -6 < x ≤ -2: Open circle at -6, closed circle at -2, shade between
6. -2.5 ≤ x ≤ -0.5: Closed circles at both ends, shade between
7. x ≤ -3: Closed circle at -3, shade to the left
8. -20 ≤ x < 80: Closed circle at -20, open circle at 80, shade between
9. -0.5 < x < 0.7: Open circles at both ends, shade between

## Extension: Finding whole numbers and prime numbers

Whole numbers are: 0, 1, 2, 3, 4, 5, ... (non-negative integers)
Prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, ...

Let me work through each inequality:

Whole Numbers Table:

1. -1 ≤ x < 3: Whole numbers in this range are 0, 1, 2
2. -22 ≤ x ≤ -19: No whole numbers (all negative)
3. 99 < x < 101: Only 100 is a whole number in this range
4. 0.8 < x < 6.9: Whole numbers are 1, 2, 3, 4, 5, 6

Prime Numbers Table:

1. 2 ≤ x < 13: Primes are 2, 3, 5, 7, 11
2. 41 < x < 53: Primes are 43, 47
3. 0 < 2x < 14: First solve for x: 0 < x < 7. Primes are 2, 3, 5
4. -22 ≤ 1 - x < -16:
- Subtract 1 from all parts: -23 ≤ -x < -17
- Multiply by -1 (flip inequalities): 23 ≥ x > 17, or 17 < x ≤ 23
- Primes in this range: 19, 23

Final Answer:

Section A:
1. x > -1
2. x < -1
3. x > 0
4. x ≥ 1
5. x ≥ -2
6. x ≤ -2
7. -1 < x < 3
8. -2 ≤ x ≤ 1
9. -2 < x ≤ 1

Section B: Draw as described above with appropriate circles and shading

Extension - Whole Numbers:
- -1 ≤ x < 3: 0, 1, 2
- -22 ≤ x ≤ -19: none
- 99 < x < 101: 100
- 0.8 < x < 6.9: 1, 2, 3, 4, 5, 6

Extension - Prime Numbers:
- 2 ≤ x < 13: 2, 3, 5, 7, 11
- 41 < x < 53: 43, 47
- 0 < 2x < 14: 2, 3, 5
- -22 ≤ 1 - x < -16: 19, 23