Question

1. {x | x < 1/2}

Explanation:

Step1: Identify the inequality

The set is given as $\{x | x < \frac{1}{2}\}$, which means we need to represent all real numbers less than $\frac{1}{2}$ on the number line.

Step2: Locate the point $\frac{1}{2}$

On the number line, find the position of $\frac{1}{2}$ (which is 0.5).

Step3: Draw the graph

Since $x$ is less than $\frac{1}{2}$, we use an open circle at $\frac{1}{2}$ (because $\frac{1}{2}$ is not included in the set) and draw an arrow to the left (towards negative infinity) to represent all numbers less than $\frac{1}{2}$.

Answer:

To graph $\{x | x < \frac{1}{2}\}$ on a number line:

1. Find the point $\frac{1}{2}$ (or 0.5) on the number line.
2. Place an open circle at $\frac{1}{2}$ (indicating $\frac{1}{2}$ is not in the solution set).
3. Draw an arrow starting from the open circle and pointing to the left (towards smaller numbers) to represent all real numbers less than $\frac{1}{2}$.