Graph the solutions of the inequality on a number line. \[ x<6 \]

Certainly! Let's graph the inequality \( x < 6 \) on a number line. ### Number Line Representation: ``` <----|----|----|----|----|----|----> 2 4 6 8 10 12 o====================> ``` ### Explanation: 1. **Open Circle at 6:** - Since the inequality is **\( x < 6 \)** (strictly less than), we use an **open circle** at \( x = 6 \) to indicate that 6 is **not** included in the solution set. 2. **Shade to the Left:** - The shading extends to the **left** of 6, representing all numbers less than 6. ### Detailed Illustration: ``` <----|----|----|----|----|----|----> 2 4 6 8 10 12 o====================> ``` - **`o` (Open Circle)** at 6: Indicates 6 is not included. - **`====================>`**: Arrow pointing to the left showing all values less than 6 are part of the solution. ### Solution Set: All real numbers **less than 6** satisfy the inequality \( x < 6 \). In interval notation, this is written as: \[ (-\infty, 6) \] ### Summary: - **Inequality:** \( x < 6 \) - **Graph:** Open circle at 6, shading to the left. - **Solution Set:** All real numbers less than 6. If you have any further questions or need additional assistance with graphing inequalities, feel free to ask!