Write the four inequalities that define the unshaded region R on the XOY plane below.

let's define the unshaded region R with inequalities. To define the unshaded region R, we need to identify the four boundary lines and determine the correct inequality for each. Step 1: Identify the vertical boundary line. There is a solid vertical line at x = 2. The unshaded region R is to the right of this line. The inequality is x 2. Step 2: Identify the horizontal boundary lines. There is a solid horizontal line at y = 5. The unshaded region R is below this line. The inequality is y 5. There is another solid horizontal line at y = -1. The unshaded region R is above this line. The inequality is y -1. Step 3: Identify the slanted boundary line. This solid line passes through the points (0, 9) and (9, 0). We can find its equation. The slope m = (0 - 9)/(9 - 0) = (-9)/(9) = -1. The y-intercept is 9. So, the equation of the line is y = -x + 9, which can be rewritten as x + y = 9. The unshaded region R is below this line. To confirm the inequality, pick a point in region R, for example, (4, 2). Substitute into x + y: 4 + 2 = 6. Since 6 < 9, the inequality is x + y 9. The four inequalities that define the unshaded region R are: x 2 y 5 y -1 x + y 9 What's next?