Question

graphing inequalities in two variables
determine which ordered pairs are part of the solution set for each inequality.

1. ( 3x + y geq 6, {(4, 3), (-2, 4), (-5, -5), (3, -3)}
2. ( y geq x + 3, {(0, 3), (-3, 2), (3, -2), (4, 3)}
3. ( 4x - 2y < 5, {(4, -4), (3, 5), (5, 2), (-3, 4)}

graph each inequality.

1. ( 2y - x < -4 )
2. ( 2x - 2y geq 8 )
3. ( 4y > 2x - 3 )

(images of coordinate grids for problems 4,5,6)
use a graph to solve each inequality.

1. ( -5 leq x - 9 )
2. ( 6 > \frac{2}{5}x + 5 )
3. ( \frac{1}{2} > -2x + \frac{7}{2} )

(images of coordinate grids for problems 7,8,9)

1. moving a moving van has an interior height of 7 feet (84 inches). you have boxes in 12 inch and 15 inch heights, and want to stack them as high as possible to fit. write an inequality that represents this situation.
2. budgeting satchi found a used bookstore that sells pre - owned dvds and cds. dvds cost $9 each, and cds cost $7 each. satchi can spend no more than $35.

a. write an inequality that represents this situation.
b. does satchi have enough money to buy 2 dvds and 3 cds?

Explanation:

Step1: Analyze the inequality for ordered pairs

We check each ordered pair \((x,y)\) in the inequality \(3x + y\geq6\).

• For \((4,3)\): Substitute \(x = 4,y = 3\) into \(3x + y\), we get \(3\times4+3=12 + 3=15\), and \(15\geq6\), so \((4,3)\) is a solution.
• For \((-2,4)\): Substitute \(x=-2,y = 4\) into \(3x + y\), we get \(3\times(-2)+4=-6 + 4=-2\), and \(-2<6\), so \((-2,4)\) is not a solution.
• For \((-5,-5)\): Substitute \(x = - 5,y=-5\) into \(3x + y\), we get \(3\times(-5)+(-5)=-15-5=-20\), and \(-20<6\), so \((-5,-5)\) is not a solution.
• For \((3,-3)\): Substitute \(x = 3,y=-3\) into \(3x + y\), we get \(3\times3+(-3)=9 - 3=6\), and \(6\geq6\), so \((3,-3)\) is a solution.

Step2: Conclusion

The ordered pairs that are part of the solution set are \((4,3)\) and \((3,-3)\).

Answer:

The ordered pairs \((4,3)\) and \((3,-3)\) are part of the solution set.