Direction: Sketch the graph and write the solution set in interval notation the given inequality. 1. \( x-3<1 \)

To solve the inequality \( x - 3 < 1 \) and represent its solution graphically and in interval notation, follow these steps: ### Step 1: Solve the Inequality \[ x - 3 < 1 \] Add 3 to both sides to isolate \( x \): \[ x < 4 \] ### Step 2: Write the Solution in Interval Notation The solution \( x < 4 \) includes all real numbers less than 4. In interval notation, this is expressed as: \[ (-\infty, 4) \] *Note:* The parenthesis around 4 indicates that 4 is **not** included in the solution set. ### Step 3: Sketch the Graph on a Number Line Below is a representation of the solution on a number line: ``` <---|-----|-----|-----|-----|-----|---> 0 1 2 3 4 5 ``` - **Open Circle at 4:** Place an open circle (○) at the number 4 to show that 4 is not included. - **Shade to the Left:** Shade the entire line to the left of 4 to represent all numbers less than 4. **Graphical Representation:** ``` <---|-----|-----|-----|-----○=====> 0 1 2 3 4 5 ``` - The open circle at 4 indicates \( x = 4 \) is not part of the solution. - The arrow pointing to the left from 4 represents all real numbers less than 4. ### Summary - **Solution Set:** \( x < 4 \) - **Interval Notation:** \( (-\infty, 4) \) - **Graph:** A number line with an open circle at 4 and shading extending to the left.