Two-Variable Linear Inequalities
Which of the following graphs represents the inequality ?
a
is a solution to 4y - 2x < 8. is a solution to 2y + 0.1x > -0.4.
(1,2) (0,0)
What is a solution to the inequality?
(4,1)
Vishal wants to burn at least 2,400 calories during his weekly workouts. He burns 400 calories per hour swimming and 600 calories per hour rollerblading. He decides to swim for 3 hours this week. How many hours must he rollerblade to reach his goal? Let x be the number of hours Vishal swims and y be the number of hours he rollerblades. Given that Vishal swims 3 hours, the number of hours spent rollerblading is represented by y > 2
y >=2
Mika wants to buy two types of cookies. The vanilla cookies cost $4 per box and the peanut butter cookies cost $6 per box. She wants to spend no more than $30 and to buy at least one box of each type of cookie. Think about the inequality that represents the given scenario if x represents the boxes of vanilla cookies. Select all of the following statements that are true about the graph representing the boxes of cookies Mika can buy.
a,b
Select all of the ordered pairs that are solutions to the inequality: 50x + 150y > 1500
a,d
This inequality means that he must rollerblade ___ hours.
at least 2
Ezra works two summer jobs to save for a laptop that costs at least $1100. He considers adjusting his rates to the following:Lawn care: $250 per lawn for the summerDog walking: $300 per dog for the summerWhich inequality represents this situation?
b
Which expression represents the revenue from performing x weekday shows and y weekend shows?
b. 50x + 150y
The band schedules 6 weekend shows and needs to perform enough weekday shows to make more than $1,500. Which inequality models this situation?
c
Which graph models the solution set of 50x + 150y > 1500?
c
A band charges $150 per weekend show and $50 per weekday show. The band needs to generate more than $1,500 in revenue. Use the graph to determine which of the following are solutions to the inequality.
c,d
Select all of the following ordered pairs that are solutions to the inequality.
c,d,e
Select all of the following ordered pairs that are in the solution set of the inequality shown.
c,e,f
The revenue generated by the band is given by the expression 50x+150y. The revenue generated by the band is given by the expression 50x + 150y.If the band plays 15 weekday shows and 6 weekend shows will they exceed their goal of $1500 or fall short? By how much?
c. exceed by $150
Choose the inequality that relates the manager's number of gigs and monthly rate to the last month's earnings.
d
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr for lawn care and $10/hr to walk dogs. Let x represent the hours he spends on lawn care and y represent the hours he spends walking dogs.Which inequality represents this situation?
d
If Ezra limits himself to 1 dog, how many lawns does he have to care for to reach his goal?
d
What does the solution x > 12 mean?
d
The ordered pair (0, 0) is not a reasonable solution to the inequality because the manager X makes more than $20 per month always books at least one show
earns at least a monthly rate.
Now suppose b stays the same. Then, a must be ___ than its previous value to satisfy the new inequality.
greater than
To see how the solution set changes, suppose the coordinate pair (a, b) satisfies the original inequality. If a stays the same, b must be less ____ its previous value to satisfy the new inequality.
greater than
If Ezra works less than or equal to 50 hours doing lawn care, he must spend at least ___ hours walking dogs
35
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. This situation is modeled by: 15x + 10y ≥ 1100. Suppose Ezra decides to also spend more than $80 on a printer. The inequality becomes 15x + 10y ___ ____
> 1180
Ezra works two summer jobs to save for a laptop that costs at least $1100. He decides to adjust his rates to $250 per lawn (x) for the summer and $300 per dog (y) for the summer, and to limit himself to 2 dogs.Describe how to find a solution graphically.
Graph in the first quadrant because x and y are nonnegative. Determine and graph the inequality that represents the situation . Shade the half-plane that does not include the origin since (0, 0) does not satisfy the inequality. Draw a horizontal line at y = 2 for 2 dogs. Solutions lie on or below the part of the horizontal line that is in the shaded region.
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: Explain how to graph the solution set.
Graph only the first quadrant since x and y must be nonnegative. The graph has a solid boundary line. Graph the boundary line using the related equation, y = -1.5x + 110. Choose a test point such as (0, 0) to determine which half-plane to shade. If the test point is true, shade that side of the boundary line. Shade to the right of the solid boundary line.
Is the solution to a two-variable inequality always a solution of the related function? Explain.
Not always. If the inequality does not have "or equal to," then the boundary line is dashed and not in the solution.
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. Recall the inequality that represents this situation: .Is (60, 20) a solution? How do you know? What does this point represent?
The coordinate pair (60, 20) is a solution because it satisfies the inequality . The coordinate pair (60, 20) is a solution because Ezra earns 60 x $15 = $900 mowing lawns and 20 x $10 = $200 walking dogs, for a total of $1100. Ezra can spend 60 hours mowing lawns and 20 hours walking dogs to earn enough money for the laptop
Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dogs. He currently charges in half-hour intervals.Recall the inequality that represents this situation: .Ezra decides to charge per dog instead of per hour. How does the solution set change? What are the limitations on x and y? Explain.
The limitations on y-values changed from nonnegative multiples of one-half to whole numbers, since Ezra cannot walk a fractional number of dogs. The limitations on x-values did not change and must be nonnegative multiples of one-half, since Ezra cannot work negative hours and charges by the half-hour.
Giuseppe wants to try two different kinds of soup. One soup has 60 mg sodium per ounce. The other has 80 mg sodium per ounce. Giuseppe wants to consume no more than 1,000 mg sodium. Which inequality represents the situation?
a
How is the graph of the solution affected?
a,c
What is the inequality shown in the graph?
c