Solve the inequality and graph the solution.

Question

Solve the inequality and graph the solution.
y
2
>
–
2
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

GPT-4o mini · Answer

To solve the inequality $y^2 > -2$, we start by analyzing the inequality itself. 1. **Understanding the inequality:** The expression $y^2$ represents a square of $y$. The minimum value of $y^2$ is $0$ (when $y = 0$), which means $y^2$ cannot be negative. Therefore, $y^2 > -2$ is always true since $y^2$ will always be greater than or equal to $0$. 2. **Conclusion:** The inequality $y^2 > -2$ holds for all real numbers $y$. 3. **Graphing the solution:** Since the solution encompasses all real numbers, we can represent this on a number line. - **Graph:** You would draw a line that goes infinitely in both directions (to the left and right), indicating that every point is part of the solution set. - **Endpoints:** As there are no restrictions, we do not have any endpoints to plot, nor do we have any points to change from closed to open. Thus, the final graphical representation would show a complete line extending in both directions with no endpoints or restrictions. Essentially, you would not need to delete any middle segment as the entire line represents the solution. ### Final Summary: The solution to the inequality $y^2 > -2$ is all real numbers. The graph is an unbroken line extending infinitely in both directions.