Inequalities with number lines
key notes:
| 🔢 What Are Inequalities? |
- Inequality means “not equal”.
- It shows how two numbers compare:
👉 Is one number greater than, less than, or equal to another?
| 🧠 Symbols of Inequality |
| Symbol | Meaning | Example | Read as |
|---|---|---|---|
> | Greater than | 7 > 3 | 7 is greater than 3 |
< | Less than | 2 < 6 | 2 is less than 6 |
= | Equal to | 5 = 5 | 5 is equal to 5 |
🎯 Tip: The open side of the symbol always faces the bigger number.
| 📍 What is a Number Line? |
- A number line is a straight line with numbers placed in order.
- It helps us to see the value of numbers and compare them easily.
Example:
markdownCopyEdit←───|───|───|───|───|───|───→
1 2 3 4 5 6
- Numbers to the right are greater.
- Numbers to the left are lesser.
| 👁️🗨️ Using Number Lines to Compare Numbers |
Compare 4 and 6 using the number line:
vbnetCopyEdit←───|───|───|───|───|───|───→
2 3 4 5 6 7
4 < 6 ✅
(Because 4 is to the left of 6)
Compare 8 and 5:
vbnetCopyEdit←───|───|───|───|───|───|───→
4 5 6 7 8 9
8 > 5 ✅
(Because 8 is to the right of 5)
| ✍️Practice Time |
Use the number line to answer:
- Which is greater: 3 or 7? → _______
- Is 9 < 6? → Yes / No
- 10 ____ 12 → Fill in the correct symbol
- 8 is to the _______ of 6
- Which number is smaller: 2 or 5? → _______
| 🧠 Key Points to Remember |
- Greater than ( > ) → Big number is on the left
- Less than ( < ) → Small number is on the left
- Use number lines to visually compare values
- Numbers increase to the right and decrease to the left
| 🎯 Real-Life Example |
Measuring height or distance
Comparing scores in a game
Comparing prices at a shop
Learn with an example
▶️ Which number line shows the numbers that are less than or equal to 1?
- Look at the first number line.
The number line has a filled-in circle on 1. That means the inequality includes the number 1.
The number line also shows an arrow pointing to the left, where numbers are less than 1. That means the inequality also includes numbers less than 1.
Together, the circle and arrow show less than or equal to 1. This is the correct number line.
Now look at the second number line.
The number line has an open circle on 1. That means the inequality does not include the number 1.
The number line also shows an arrow pointing to the left, where numbers are less than 1. That means the inequality includes numbers less than 1.
Together, the circle and arrow show less than 1. This is not the correct number line.
▶️ Which number line shows the numbers that are less than 7?
- Look at the first number line.
The number line has an open circle on 7. That means the inequality does not include the number 7.
The number line also shows an arrow pointing to the left, where numbers are less than 7. That means the inequality includes numbers less than 7.
Together, the circle and arrow show less than 7. This is the correct number line.
Now look at the second number line.
The number line has an open circle on 8. That means the inequality does not include the number 8.
The number line also shows an arrow pointing to the left, where numbers are less than 8. That means the inequality includes numbers less than 8.
Together, the circle and arrow show less than 8. This is not the correct number line.
🗼 Which inequality does this number line show?
- greater than or equal to 2
- less than or equal to 3
- less than or equal to 4
- less than 3
- The number line has an open circle on 3. That means the inequality does not include the number 3.
- The number line also shows an arrow pointing to the left, where numbers are less than 3. That means the inequality includes numbers less than 3.
- Together, the circle and arrow show less than 3.
Let’s practice!
