7. On the grid, clearly label the region which satisfies all three inequalities below \( \begin{array}{lll}\text { 5. } \\ x \leq 2 & y<2 x-2 & x+y+2>0\end{array} \)

Since I cannot plot the graph directly, I will describe how to visualize the inequalities step by step. 1. **Graph the line \( x = 2 \)**: - Draw a vertical dashed line at \( x = 2 \) (dashed because the inequality is \( \leq \), which includes the line). 2. **Graph the line \( y = 2x - 2 \)**: - This line has a y-intercept of -2 and a slope of 2. - Plot the points (0, -2) and (2, 2) to draw the line. - Use a dashed line since the inequality is \( < \). - Shade the area below this line. 3. **Graph the line \( y = -x - 2 \)**: - This line has a y-intercept of -2 and a slope of -1. - Plot the points (0, -2) and (-2, 0) to draw the line. - Use a dashed line since the inequality is \( > \). - Shade the area above this line. ### Final Region The region that satisfies all three inequalities will be: - To the left of the line \( x = 2 \). - Below the line \( y = 2x - 2 \). - Above the line \( y = -x - 2 \). ### Labeling the Region You can label the intersection area where all shaded regions overlap. This area will be bounded by the lines and will be the solution to the system of inequalities. If you have graphing software or graph paper, you can follow these steps to visualize the solution accurately.