1. **State the problem:** We are given three inequalities involving $x$ and asked to understand their graph representations. 2. **Inequality a:** $x < \sqrt{3}$ - This means $x$ can be any number less than $\sqrt{3}$ but not equal to $\sqrt{3}$. - The graph shows an open circle at $\sqrt{3}$ and a ray extending left towards negative infinity. 3. **Inequality b:** $x \geq -5$ - This means $x$ can be any number greater than or equal to $-5$. - The graph shows a closed dot at $-5$ and a ray extending right towards positive infinity. 4. **Inequality c:** $-2 \leq x < 2$ - This means $x$ is between $-2$ and $2$, including $-2$ but excluding $2$. - The graph shows a closed dot at $-2$, an open circle at $2$, and a segment connecting them. 5. **Summary:** - Open circle means the endpoint is not included. - Closed dot means the endpoint is included. - Rays extend infinitely in one direction. - Segments connect two points including or excluding endpoints as specified. Final answers are the inequalities as given, correctly graphed as described.