Question

1. x > -2

y < 3
y ≥ 2x - 1

Explanation:

Step1: Analyze \( x > -2 \)

This inequality represents all points to the right of the vertical line \( x = -2 \) (dashed line since it's \( > \), not \( \geq \)).

Step2: Analyze \( y < 3 \)

This inequality represents all points below the horizontal line \( y = 3 \) (dashed line since it's \( < \), not \( \leq \)).

Step3: Analyze \( y \geq 2x - 1 \)

This inequality represents all points on or above the line \( y = 2x - 1 \) (solid line since it's \( \geq \)).

Step4: Find the intersection

The solution region is where all three inequalities overlap: to the right of \( x = -2 \), below \( y = 3 \), and on or above \( y = 2x - 1 \). To graph, plot the lines: \( x = -2 \) (dashed, vertical), \( y = 3 \) (dashed, horizontal), \( y = 2x - 1 \) (solid, with slope 2 and y - intercept - 1). Shade the area that satisfies all three.

Answer:

The solution is the region defined by \( x > -2 \), \( y < 3 \), and \( y \geq 2x - 1 \), which can be graphed by shading the area that meets all three inequalities.