One Variable Inequalities Notes and Worksheets - Lindsay Bowden - Free Printable

Let's solve the problem step by step based on the worksheet titled "Graphing One Variable Inequalities Notes."

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🔹 Step 1: Fill in the Blanks

The worksheet starts with definitions:

> inequality – a comparison between values that involves one of the following symbols:
> - > : greater than
> - ≥ : greater than or equal to
> - < : less than
> - ≤ : less than or equal to

✔ So, the first blank should be: comparison

> graphing an inequality – we can graph a one-variable inequality on a number line.

✔ The second blank: number

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🔹 Understanding the Symbols (Key to Graphing)

There are two types of dots used on the number line:
- Open circle (○) → Used for < or >, meaning the endpoint is not included
- Closed circle (●) → Used for ≤ or ≥, meaning the endpoint is included

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🔹 Now Let’s Graph Each Inequality

We'll go through each example and explain how to graph it.

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#### ✔ 1. $ x \leq 0 $

- This means x is less than or equal to 0
- Use a closed circle at 0 (because of the "equal to")
- Shade to the left of 0 (all numbers less than 0)

📌 Graph:
```
<---●===================>
-5 -4 -3 -2 -1 0 1 2 3 4 5
```

- Closed circle at 0, shaded to the left.

---

#### ✔ 2. $ x > 4 $

- This means x is greater than 4
- Use an open circle at 4 (since it's not included)
- Shade to the right of 4

📌 Graph:
```
====================○---->
-5 -4 -3 -2 -1 0 1 2 3 4 5
```

- Open circle at 4, shaded to the right.

---

#### ✔ 3. $ x \leq -2 $

- This means x is less than or equal to -2
- Use a closed circle at -2
- Shade to the left of -2

📌 Graph:
```
<---●==================>
-5 -4 -3 -2 -1 0 1 2 3 4 5
```

- Closed circle at -2, shaded to the left.

---

#### ✔ 4. $ x \geq -1 $

- This means x is greater than or equal to -1
- Use a closed circle at -1
- Shade to the right of -1

📌 Graph:
```
===================●---->
-5 -4 -3 -2 -1 0 1 2 3 4 5
```

- Closed circle at -1, shaded to the right.

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🔹 Final Answer Summary

| Problem | Graph Description |
|--------|-------------------|
| 1. $ x \leq 0 $ | Closed circle at 0, shade left |
| 2. $ x > 4 $ | Open circle at 4, shade right |
| 3. $ x \leq -2 $ | Closed circle at -2, shade left |
| 4. $ x \geq -1 $ | Closed circle at -1, shade right |

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✔ How to Remember:

- Closed circle (●) = includes the number (≤ or ≥)
- Open circle (○) = does not include the number (< or >)
- Shade direction:
- For < or ≤, shade left
- For > or ≥, shade right

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Let me know if you'd like this turned into a printable answer key or need help with more inequalities!