a salad made such that the difference between twice the ounces of greens and the ounces of carrots is at…

Answer:

We first need to set up the system of inequalities. Let (x) be the ounces of greens and (y) be the ounces of carrots. The first - condition: "the difference between twice the ounces of greens and the ounces of carrots is at least 3" gives us the inequality (2x - y\geq3), which can be rewritten as (y\leq2x - 3). The boundary line (y = 2x-3) has a y - intercept of (- 3) and a slope of 2. Since the inequality is (y\leq2x - 3), we will have a solid line (because of (\geq)) and shade below the line. The second - condition: "the sum of the ounces of greens and twice the ounces of carrots is less than 4" gives us the inequality (x + 2y<4), which can be rewritten as (y<-\frac{1}{2}x + 2). The boundary line (y=-\frac{1}{2}x + 2) has a y - intercept of 2 and a slope of (-\frac{1}{2}). Since the inequality is (y<-\frac{1}{2}x + 2), we will have a dashed line (because of (<)) and shade below the line. We then need to match these characteristics with the given graphs.

Explanation:

Step1: Set up first inequality

Let (x) be ounces of greens and (y) be ounces of carrots. (2x - y\geq3) is rewritten as (y\leq2x - 3).

Step2: Analyze first - inequality boundary

The line (y = 2x-3) has slope (m = 2) and y - intercept (b=-3). Shade below for (y\leq2x - 3), solid line.

Step3: Set up second inequality

(x + 2y<4) is rewritten as (y<-\frac{1}{2}x + 2).

Step4: Analyze second - inequality boundary

The line (y=-\frac{1}{2}x + 2) has slope (m =-\frac{1}{2}) and y - intercept (b = 2). Shade below for (y<-\frac{1}{2}x + 2), dashed line.

Step5: Match with graphs

Match the shading and line - types (solid/dashed) of the two inequalities with the given graphs.