The inequality shown in the image is $y < |x| + 3$. Here's how this inequality can be interpreted and graphed:

Step-by-step Analysis:

1. Absolute Value Function: The equation $y = |x| + 3$ represents a V-shaped graph, with the vertex at $(0, 3)$, and the arms of the "V" have slopes of $+1$ and $-1$ respectively. This is the boundary line of the inequality.

2. Inequality $y < |x| + 3$:

   • The inequality $y < |x| + 3$ means we are interested in the region below the V-shaped curve. This is because the inequality symbol is "<", not "≤".
   • The boundary $y = |x| + 3$ is not included, so the line itself is dashed to indicate that points on this line do not satisfy the inequality.

3. Graphing:

   • Draw the V-shaped graph for $y = |x| + 3$ with a dashed line.
   • Shade the region below this V, because the inequality is $y < |x| + 3$.

Verification with the Image:

From the image, the graph shows a V-shape with a dashed line, and the arrows point downward, indicating that the region below the V is the solution, which is correct based on the inequality.

Would you like more details on how to handle absolute value inequalities, or do you have any specific questions?

Questions to consider:

1. How would the graph change if the inequality was $y \leq |x| + 3$?
2. What if the equation was $y > |x| + 3$? How would you graph it?
3. Can you identify the vertex of any general equation $y = |x| + c$?
4. How do you solve absolute value inequalities algebraically?
5. What are some real-life applications of absolute value functions?

Tip:

Remember, the inequality symbol determines whether you shade above or below the graph. If it's "<" or ">", shade below or above respectively.