Part 1 of 2 Solve the inequality \( x+5>8 \). Then graph the solutions. What are the solutions? Select the correct choice below and fill in the answer box to complete your choice.

To solve the inequality \( x + 5 > 8 \), follow these steps: ### Step 1: Isolate the Variable \( x \) Subtract 5 from both sides of the inequality to isolate \( x \): \[ \begin{align*} x + 5 &> 8 \\ x + 5 - 5 &> 8 - 5 \\ x &> 3 \end{align*} \] ### Solution \[ \boxed{x > 3} \] ### Graphing the Solution To graph the inequality \( x > 3 \) on a number line: 1. **Draw a Number Line:** - Represent a horizontal line with evenly spaced marks indicating numbers. 2. **Plot the Boundary Point:** - Place an open circle (○) at \( x = 3 \) to show that 3 is **not** included in the solution. 3. **Shade the Solution Region:** - Shade the portion of the number line to the **right** of the open circle at 3, indicating all real numbers greater than 3 are solutions. **Visualization:** ``` <-------|------○======> 3 ``` - The open circle at 3 signifies \( x = 3 \) is not included. - The arrow and shading to the right of 3 represent all values where \( x > 3 \). ### Summary - **Inequality Solution:** \( x > 3 \) - **Graph:** Open circle at 3 with shading to the right on the number line.