Let’s solve each inequality step by step and graph them on the number line.
---
Problem 10: 0 < x < 4
This means x is greater than 0 AND less than 4.
So, x can be any number between 0 and 4 — but NOT including 0 or 4.
On the number line:
- We put an
open circle at 0 (because it’s not included).
- We put an
open circle at 4 (because it’s not included).
- Then we draw a line connecting them to show all numbers in between are part of the solution.
✔ Graph matches what’s shown: open circles at 0 and 4, blue line between them.
---
Problem 11: -3 < x < 1
This means x is greater than -3 AND less than 1.
So, x can be any number between -3 and 1 — but NOT including -3 or 1.
On the number line:
- Open circle at -3 (not included)
- Open circle at 1 (not included)
- Green line between them
✔ Graph matches: open circles at -3 and 1, green line between.
---
Problem 12: -4 ≤ x < -1
This means x is greater than OR EQUAL TO -4, AND less than -1.
So, x includes -4, but does NOT include -1.
On the number line:
-
Closed circle at -4 (because it IS included — note the “≤” sign)
-
Open circle at -1 (because it’s NOT included — note the “<” sign)
- Red line between them
✔ Graph matches: closed red circle at -4, open red circle at -1, red line between.
---
All three graphs are correctly drawn according to the inequalities.
Final Answer: All graphs are correct as shown.
Parent Tip: Review the logic above to help your child master the concept of graphing inequalities on a number line.
