$$ 1 \leqslant \quad $$ Express the following inequality a) using a number line, b) in interval notation, and $$ c $$ ) as a solution set (use set builder notation).

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It appears you're working with the inequality $$ 1 \leq x $$. Let's express this inequality in the three requested formats:

### a) Using a Number Line

A number line representation of $$ 1 \leq x $$ would show all numbers from **1** to positive infinity, including **1** itself. Here's a textual description:

- **Closed Circle at 1**: Indicates that **1** is included in the solution set.
- **Shading to the Right**: Represents all numbers greater than or equal to **1**.

```
<----|======================>
     1
```

*Note: The "=" signs represent shading extending to the right from **1**, and the "|" at **1** is a closed circle.

### b) In Interval Notation

Interval notation compactly represents the set of solutions. For $$ 1 \leq x $$:

$$
[1, \infty)
$$

- **[1,** : The square bracket **[** indicates that **1** is included.
- **$$\infty)$$** : The parenthesis **)** indicates that infinity is not a specific number and thus not included.

### c) As a Solution Set (Set Builder Notation)

Set builder notation describes the set of all elements **x** that satisfy the inequality. For $$ 1 \leq x $$:

$$
\{\, x \mid x \geq 1 \,\}
$$

- **$$\{\, x \mid$$** : Represents the set of all **x** such that the condition that follows is true.
- **$$x \geq 1 \,\}** : The condition that **x** is greater than or equal to **1**.

---

**Summary:**

a) **Number Line**: Closed circle at 1 with shading to the right.

b) **Interval Notation**: $$[1, \infty)$$

c) **Set Builder Notation**: $$\{\, x \mid x \geq 1 \,\}$$
a) **Number Line**: A closed circle at 1 with shading extending to the right. b) **Interval Notation**: $$[1, \infty)$$ c) **Set Builder Notation**: $$\{\, x \mid x \geq 1 \,\}$$

\( 1 \leqslant \quad \) Express the following inequality a) using a number line, b) in interval notation, and \( c \) ) as a solution set (use set builder notation).

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