Let's solve each problem step by step from the worksheet titled
"Practice 2-8: Inequalities and Their Graphs".
---
1. The total is less than sixteen.
We are told that "the total" is less than 16.
Let’s assume the variable $ x $ represents the total.
So, the inequality is:
$$
x < 16
$$
✔ Answer: $ x < 16 $
---
2. The price $ p $ is less than or equal to $25.
This directly translates to:
$$
p \leq 25
$$
✔ Answer: $ p \leq 25 $
---
3. A number $ n $ is negative.
A negative number is less than zero:
$$
n < 0
$$
✔ Answer: $ n < 0 $
---
4. Graph the solution of the inequality on a number line:
The number line shows a
closed circle at -2 and shading to the
right.
- Closed circle means the value is included.
- Shading to the right means values greater than or equal to -2.
So, the inequality is:
$$
x \geq -2
$$
✔ Answer: $ x \geq -2 $
---
5. Number line shows an open circle at 0 and shading to the left.
- Open circle at 0 → 0 is
not included
- Shading to the left → values
less than 0
So:
$$
x < 0
$$
✔ Answer: $ x < 0 $
---
6. Number line has a closed circle at -1 and shading to the left.
- Closed circle at -1 → includes -1
- Shading to the left → values less than or equal to -1
So:
$$
x \leq -1
$$
✔ Answer: $ x \leq -1 $
---
7. Number line has an open circle at 3 and shading to the right.
- Open circle at 3 → does not include 3
- Shading to the right → values greater than 3
So:
$$
x > 3
$$
✔ Answer: $ x > 3 $
---
8. Graph the solution of $ x < -2 $ on a number line.
- Since it's
strictly less than, use an
open circle at $-2$
- Shade to the
left (all numbers less than -2)
✔ Graph: Open circle at -2, shaded to the left.
---
9. Graph the solution of $ x \geq -1 $ on a number line.
- Closed circle at $-1$ (since it's "greater than or equal")
- Shade to the
right
✔ Graph: Closed circle at -1, shaded to the right.
---
10. $ z > -1 $
- Open circle at $-1$
- Shade to the
right
✔ Graph: Open circle at -1, shaded to the right.
---
11. $ p \geq 4 $
- Closed circle at 4
- Shade to the
right
✔ Graph: Closed circle at 4, shaded to the right.
---
12. You spend less than $20 on a book. Let $ b $ be the cost of the book.
"Less than $20" → $ b < 20 $
✔ Answer: $ b < 20 $
---
13. You have $430 to spend on lunch. Let $ c $ be the cost of your lunch.
You can spend
up to $430, so the cost can be
less than or equal to $430.
$$
c \leq 430
$$
✔ Answer: $ c \leq 430 $
---
✔ Final Answers:
| Problem | Answer |
|--------|--------|
| 1 | $ x < 16 $ |
| 2 | $ p \leq 25 $ |
| 3 | $ n < 0 $ |
| 4 | $ x \geq -2 $ |
| 5 | $ x < 0 $ |
| 6 | $ x \leq -1 $ |
| 7 | $ x > 3 $ |
| 8 | Graph: open circle at -2, shade left |
| 9 | Graph: closed circle at -1, shade right |
| 10 | Graph: open circle at -1, shade right |
| 11 | Graph: closed circle at 4, shade right |
| 12 | $ b < 20 $ |
| 13 | $ c \leq 430 $ |
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Let me know if you'd like a visual representation of the graphs!
Parent Tip: Review the logic above to help your child master the concept of inequalities and their graphs worksheet.
