Inequalities

Which is the graph of the linear inequality y ≥ −x − 3?

A.

Which linear inequality is represented by the graph?

B. y < 1/3x-4

Which linear inequality is represented by the graph?

B. y > 3x + 2

Which linear inequality is represented by the graph?

B. y < 1/2x+3

Which statements are true about the linear inequality y &gt; x – 2? Check all that apply.

-The graph of y > x – 2 is a dashed line. -One solution to the inequality is (0, 0). -The graph intercepts the y-axis at (0, -2).

Which is the graph of the linear inequality 1/2x – 2y &gt; -6?

D.

The solutions to the inequality y ≤ 2x − 4 are shaded on the graph. Which point is a solution?

C. (3, 2)

Which linear inequality is represented by the graph?

A. y<1/2x+2

Which is the graph of linear inequality 2y &gt; x – 2?

C.

Which description of the graph of the linear equality y ≥ 7x – 4 is correct?

B. The graph will be a solid line with a y-intercept of negative four and a slope of seven. The graph will be shaded above the line.

Which is the graph of the linear inequality 2x – 3y &lt; 12?

C.

Which linear inequality is represented by the graph?

C. y>2/3x+3

The solutions to the inequality y ≤ −x + 1 are shaded on the graph. Which point is a solution?

B. (3, -2)

The solutions to the inequality y &gt; −3x + 2 are shaded on the graph. Which point is a solution?

B. (2, 0)

Hamburgers cost $2.50 and cheeseburgers cost $3.50 at a snack bar. Ben has sold no more than $30 worth of hamburgers and cheeseburgers in the first hour of business. Let x represent the number of hamburgers and y represent the number of cheeseburgers. The inequality 2.50x + 3.50y ≤ 30 represents the food sales in the first hour.

If Ben has sold 4 cheeseburgers, what is the maximum value of hamburgers Ben could have sold?

6

Which shows the graph of the solution set of 3y – 2x &gt; -18?

D.

Which shows the graph of the solution set of y &gt; -1/2x – 3?

B.

Which shows the graph of the solution set of y &lt; -4x + 3?

D.

Lola bought x pencils that cost $0.25 each and y erasers that cost $0.50. She spent less than $3. Which graph represents Lola’s purchase?

C.

Which shows the graph of the solution set of x + 2y &gt; 4?

C.

Which shows the graph of the solution set of 2x + y &lt; 4?

C.

At lunch, Kira eats either a burrito containing 490 milligrams of sodium or a peanut butter sandwich containing 700 milligrams of sodium. Her doctor told her to reduce her sodium to no more than 4,000 milligrams per week. Which inequality represents x, the number of microwave burritos, and y, the number of peanut butter sandwiches, she can eat each week?

B. 490x + 700y ≤ 4000

Last year, Jess saw x dramas and y comedies at the movie theater. If she went to the theater no more than 8 times, which inequality best represents the number of movies she saw?

C. x + y ≤ 8

Jamaal spent x minutes today practicing his guitar and y minutes today on homework. If the total time he spent on both is 45 minutes or more, which inequality best represents his practice time?

D. x + y ≥ 45

Dan bought x pounds of potatoes for $0.85 per pound and y pounds of grapes for $1.29 per pound. The total cost was less than $5. Which inequality represents his purchase?

D. 0.85x + 1.29y < 5

A grocery bag contains x apples, each weighing 1/3 of a pound, and y pounds of grapes. The total weight of the grocery bag is less than 5 pounds. Which graph represents the possible numbers of apples and pounds of grapes that can be in the bag?

B.

On a final exam, each multiple-choice question is worth 4 points and each word problem is worth 8 points. Lorenzo needs at least 50 points on the final to earn a "B" in the class. Which inequality represents x, the number of correct multiple-choice questions, and y, the number of correct word problems, he needs to earn a "B"?

Not A or B

At an end of the year sale, Gabriela bought more than 12 bottles of hand soaps and lotions. If x represents the number of hand soaps and y represents the number of lotions she bought, which inequality best represents her purchase?

B. x + y > 12

A snack tray at a party has cheese squares with 2 grams of protein apiece and turkey slices with 3 grams of protein apiece. Which inequality represents the possible ways Nina can eat 12 or more grams of protein, if x is the number of cheese squares that she eats and y is the number of turkey slices that she eats?

C. 12 ≤ 2x + 3y

It takes Dimitri 9 minutes to make a simple bracelet and 20 minutes to make a deluxe bracelet. He has been making bracelets for longer than 120 minutes. If x represents the number of simple bracelets that he has made and y represents the number of deluxe bracelets he has made, the inequality 9x + 20y &gt; 120 represents the scenario.

Which is a possible combination of bracelets that Dimitri may have made?

D. 7 simple bracelets and 3 deluxe bracelets

Which ordered pair makes both inequalities true?

y &lt; -x + 1

y &gt; x

B. (-2,2)

Which graph shows the solution to the system of linear inequalities?

x – 4y &lt; 4

y &lt; x + 1

A.

Which system of linear inequalities is represented by the graph?

A. y > 1/3x + 3 and 3x – y > 2

Which ordered pair makes both inequalities true?

y &gt; -2x + 3

y &lt; x – 2

Not C

Which ordered pair makes both inequalities true?

y &lt; 3x – 1

y &gt; -x + 4

A. (4,0)

Irina wants to build a fence around a rectangular vegetable garden so that it has a width of at least 10 feet. She can use a maximum of 150 feet of fencing. The system of inequalities that models the possible lengths, l, and widths, w, of her garden is shown.

w ≥ 10

2l + 2w ≤ 150

Which length and width are possible dimensions for the garden?

B. l = 20 ft; w = 10 ft

Kyle asks his friend Jane to guess his age and his grandmother’s age. Kyle says his grandmother is not more than 80 years old. He says his grandmother’s age is, at most, 3 years less than 3 times his own age.

Jane writes this system of inequalities to represent k, Kyle’s age, and g, Kyle’s grandmother’s age.

Inequality 1: g &gt; 80
Inequality 2: g ≤ 3k – 3

Which inequality did Jane write incorrectly, and how could it be corrected?

A. Inequality 1 is incorrect; it should be g ≤ 80.

Consider the system of inequalities and its graph.

y ≤ -0.75x

y ≤ 3x – 2

In which section of the graph does the actual solution to the system lie?

D. 4

Which symbol could be written in both circles in order to represent this system algebraically?

y 3x

x -2

B. ≥

Which graph represents the solution to the system of inequalities?

y &gt; x – 4

y ≤ -1

B.

Which graph represents the solution to the system of inequalities?

x + y ≥ 4

2x + 3y &lt; 12

C.

Keitaro walks at a pace of 3 miles per hour and runs at a pace of 6 miles per hour. Each month, he wants to complete at least 36 miles but not more than 90 miles. The system of inequalities represents the number of hours he can walk, w, and the number of hours he can run, r, to reach his goal.

3w + 6r ≥ 36

3w + 6r ≤ 90

Which combination of hours can Keitaro walk and run in a month to reach his goal?

A. 2 hours walking; 12 hours running

Which graph represents the solution to the system of inequalities?

x + y ≤ 4

y – x ≥ 1

A.

Which system of inequalities is represented by the graph?

D. y ≥ 2x y > 1

A baker makes apple tarts and apple pies each day. Each tart, t, requires 1 apple, and each pie, p, requires 8 apples. The baker receives a shipment of 184 apples every day. If the baker makes no more than 40 tarts per day, which system of inequalities can be used to find the possible number of pies and tarts the baker can make?

D. t ≤ 40 8p + t ≤ 184

Marisol is making a rectangular wooden frame. She wants the length of the frame to be no more than 12 inches. She has less than 30 inches of wood to use. Which system of inequalities represents the possible length, l, and the possible width, w, that her frame could have?

A. l ≤ 12 2l + 2w < 30

Charlene is knitting a baby blanket. She wants its width, w, to be at least half its length, l. She estimates that she has enough yarn to put fringe around the blanket, as long as the perimeter of the blanket is no more than 180 inches. The system of inequalities shown represents the width of the blanket in inches, w, and the length in inches, l.

w ≥ 0.5l

2l + 2w ≤ 180

What is the maximum length possible for her blanket?

C. 60 inches