Sure! Let’s solve each inequality step by step and then explain how to graph the solution on the number line provided.
---
1) 3 ≤ x/4
Step 1: Multiply both sides by 4 to isolate x.
> 3 × 4 ≤ x
> 12 ≤ x
> or equivalently,
x ≥ 12
Graphing:
On the number line, place a
closed circle at 12 (because it’s “≥”, meaning 12 is included), and shade to the
right.
---
2) 17 + x ≥ 13
Step 1: Subtract 17 from both sides.
> x ≥ 13 - 17
> x ≥ -4
Graphing:
Closed circle at
-4, shade to the
right.
---
3) 16 ≥ x - 10
Step 1: Add 10 to both sides.
> 16 + 10 ≥ x
> 26 ≥ x
> or
x ≤ 26
Graphing:
Closed circle at
26, shade to the
left.
---
4) 25 > 5x
Step 1: Divide both sides by 5.
> 25 ÷ 5 > x
> 5 > x
> or
x < 5
Graphing:
Open circle at
5 (since it’s “<”, not “≤”), shade to the
left.
---
5) 1 > x + 6
Step 1: Subtract 6 from both sides.
> 1 - 6 > x
> -5 > x
> or
x < -5
Graphing:
Open circle at
-5, shade to the
left.
---
6) 2 < x/9
Step 1: Multiply both sides by 9.
> 2 × 9 < x
> 18 < x
> or
x > 18
Graphing:
Open circle at
18, shade to the
right.
---
7) 7x ≥ 35
Step 1: Divide both sides by 7.
> x ≥ 5
Graphing:
Closed circle at
5, shade to the
right.
---
8) 8 ≤ x - 14
Step 1: Add 14 to both sides.
> 8 + 14 ≤ x
> 22 ≤ x
> or
x ≥ 22
Graphing:
Closed circle at
22, shade to the
right.
---
##
✔ Final Answers Summary:
| Problem | Solution | Graph Type |
|---------|------------------|--------------------------------|
| 1 | x ≥ 12 | Closed circle at 12, shade right |
| 2 | x ≥ -4 | Closed circle at -4, shade right |
| 3 | x ≤ 26 | Closed circle at 26, shade left |
| 4 | x < 5 | Open circle at 5, shade left |
| 5 | x < -5 | Open circle at -5, shade left |
| 6 | x > 18 | Open circle at 18, shade right |
| 7 | x ≥ 5 | Closed circle at 5, shade right |
| 8 | x ≥ 22 | Closed circle at 22, shade right |
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## 📌 How to Graph on the Number Line:
-
Closed circle (●) = includes the point (used for ≤ or ≥)
-
Open circle (○) = does NOT include the point (used for < or >)
-
Shade direction:
- Right → greater than (x > a or x ≥ a)
- Left → less than (x < a or x ≤ a)
---
Let me know if you’d like me to draw the actual graphs or provide printable answer keys! 😊
Parent Tip: Review the logic above to help your child master the concept of graphing inequalities worksheet with answers.
