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

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**: \(\{\, x \mid x \geq 1 \,\}\)