Solve the inequality. Graph the results. \( x+4<-3 \)

To solve the inequality \( x + 4 < -3 \) and graph the solution, follow these steps: ### Step 1: Solve the Inequality Start with the given inequality: \[ x + 4 < -3 \] **Subtract 4 from both sides** to isolate \( x \): \[ \begin{align*} x + 4 - 4 &< -3 - 4 \\ x &< -7 \end{align*} \] **Solution:** \( x < -7 \) ### Step 2: Graph the Solution on a Number Line To graph \( x < -7 \): 1. **Draw a horizontal number line**. 2. **Mark a point** at \( -7 \) on the number line. 3. **Use an open circle** at \( -7 \) to indicate that \( -7 \) is **not included** in the solution set. 4. **Shade all numbers to the left** of \( -7 \) to represent all real numbers less than \( -7 \). #### Graph Representation: ``` <----|-----|-----|-----|-----|-----|-----|-----|-----> -10 -9 -8 -7 -6 -5 -4 -3 -2 ●----------------------------------> ``` - The **open circle (●)** at \( -7 \) shows that \( -7 \) is **not included**. - The **arrow and shading** to the left of \( -7 \) indicate all values **less than \( -7 \)** satisfy the inequality. ### Summary - **Solution:** All real numbers \( x \) such that \( x < -7 \). - **Graph:** An open circle at \( -7 \) with shading to the left on the number line.