Let's solve each inequality by graphing it on the number line. We'll go through each one step by step and explain how to represent the solution.
---
1. $ x < 1 $
- This means all numbers
less than 1.
- Since it's
strictly less than (not ≤), we use an
open circle at 1.
- Then, shade the line to the
left of 1 (all smaller numbers).
✔ Graph:
```
<---o====================>
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
o-----------------------------------
```
- Open circle at 1, shaded to the left.
---
2. $ x \geq -6 $
- This means all numbers
greater than or equal to -6.
- Since it includes -6 (≥), we use a
closed (filled) circle at -6.
- Shade to the
right of -6.
✔ Graph:
```
<===•===================>
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
•---------------------------------------
```
- Closed circle at -6, shaded to the right.
---
3. $ x \geq 4 $
- All numbers greater than or equal to 4.
- Use a
closed circle at 4.
- Shade to the
right.
✔ Graph:
```
<===•===================>
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
•------------------------------
```
- Closed circle at 4, shaded to the right.
---
4. $ x \geq 8 $
- All numbers greater than or equal to 8.
- Use a
closed circle at 8.
- Shade to the
right.
✔ Graph:
```
<===•===================>
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
•------------------------
```
- Closed circle at 8, shaded to the right.
---
5. $ x \leq 1 $
- All numbers less than or equal to 1.
- Use a
closed circle at 1 (since it includes 1).
- Shade to the
left.
✔ Graph:
```
<===•===================>
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
-------------------------•
```
- Closed circle at 1, shaded to the left.
---
✔ Summary of Rules:
| Symbol | Circle Type | Direction |
|--------|-------------|-----------|
| $ < $ | Open circle | Left |
| $ > $ | Open circle | Right |
| $ \leq $ | Closed circle | Left |
| $ \geq $ | Closed circle | Right |
---
You can now draw these graphs on the number lines provided in the worksheet using the above explanations.
Let me know if you'd like a visual version or printable guide!
Parent Tip: Review the logic above to help your child master the concept of algebra 1 graphing inequalities worksheet.
