Specific Learning Outcomes
You are required to:
- Write linear inequalities from statements
- Solve simple linear inequalities
- Represent inequalities on number lines
- Form and interpret compound inequalities
- Apply inequalities to real-life situations
What Is Found in This Topic
- Inequality symbols
- Simple inequalities
- Number line representation
- Compound inequalities
- Real-life applications
2.3 Linear Inequalities
Linear inequalities are expressions in which two linear expressions are compared using inequality symbols instead of an equal sign.
2.3.1 Inequality Symbols
| Symbol Name | Symbol | Example | In Words |
|---|---|---|---|
| Less than | < | x + 7 < 20 | x + 7 is less than 20 |
| Greater than | > | 10x > 2 + 16x | 10x is greater than 2 + 16x |
| Less than or equal to | ≤ | y ≤ 4 | y is less than or equal to 4 |
| Greater than or equal to | ≥ | x ≥ 7 | x is greater than or equal to 7 |
Example 2.10
Use inequality symbols to show the relationship:
(a) 2 and 5 (b) 7 and 5
Solution:
2 < 5
7 > 5
Example 2.11
Write inequalities to represent the statements:
- (x − 4) is less than 4 → (x − 4) < 4
- (2x + 4) is greater or equal to 6 → (2x + 4) ≥ 6
- x is greater than 2 → x > 2
- (y + 3) is less than or equal to 5 → (y + 3) ≤ 5
2.3.2 Simple Inequalities
Simple inequalities show the relationship between two quantities using only one inequality symbol.
Example 2.12
In a slaughter house, a cow is slaughtered if its weight exceeds 480 kg.
Solution:
Let the weight be x.
x > 480
400──450──480──500──▶
○════════▶
Example 2.13
Represent the inequalities:
(a) x ≤ 8
0──2──4──6──8──10──▶ ════════════●
(b) x > 5
0──2──4──5──6──8──▶
○════════▶
Example 2.14
Combine the inequalities:
(a) x ≤ 8 and x > 2 → 2 < x ≤ 8
(b) x ≥ 3 and x < 10 → 3 ≤ x < 10
Example 2.15
On a super highway, the minimum speed is 30 km/h and the maximum is 110 km/h.
Solution:
30 ≤ x ≤ 110
30──40──60──80──100──110 ●════════════════════●
🔗 Inequality Match-Up
Instructions: Read each statement and build the correct inequality.
Exercise 2.3
1. Write the inequalities:
(a) x is less than 5
x(b) x is not more than 3
x(c) x is not less than 4
x(d) x is greater than 10
x2. Minimum acceptable mass is 50 kg. Write an inequality for players not eligible.
x3. Vehicles longer than 2 metres are not accepted.
x6. Combine: x > 2 and x ≤ 5
x7. Frozen chicken weight is at least 1.2 kg and not more than 3.4 kg.
x