Free Printable Modeling Inequalities

1.

If Rosa's age is represented by R, which inequality represents the statement "Rosa is at most 29 years old"?

a)

R<29

b)

$R>29$

c)

$R\le29$

d)

$R\ge29$

2.

The sign shown above is posted in front of a roller coaster ride at the Wadsworth County Fairgrounds. If h represents the height of a rider in inches, what is a correct translation of the statement on this sign?

a)

$h<48$

b)

$h>48$

c)

$h\le48$

d)

$h\ge48$

3.

Roger is having a picnic for 78 guests. He plans to serve each guest at least one hot dog. If each package, p, contains eight hot dogs, which inequality could be used to determine how many packages of hot dogs Roger will need to buy?

a)

$p\ge78$

b)

$8p\ge78$

c)

$8+p\ge78$

d)

$78-p\ge8$

4.

Jeremy is hosting a Halloween party for 80 children. He will give each child at least one candy bar. If each bag of candy contains 18 candy bars, which inequality can be used to determine how many bags, c, Jeremy will need to buy?

a)

$18c\ge80$

b)

$18c\le80$

c)

$\frac{c}{18}\ge80$

d)

$\frac{c}{18}\le80$

5.

Carol plans to sell twice as many magazine subscriptions as Jennifer. If Carol and Jennifer need to sell at least 90 subscriptions in all, which inequality could be used to determine how many subscriptions, x, Jennifer needs to sell?

a)

$x\ge45$

b)

$2x\ge90$

c)

$2x-x\ge90$

d)

$2x+x\ge90$

6.

Mrs. Smith wrote "Eight less than three times a number is greater than fifteen" on the board. If x

represents the number, which inequality is a correct translation of this statement?

a)

$3x-8>15$

b)

$3x-8<15$

c)

$8-3x>15$

d)

$8-3x<15$

7.

An electronics store sells DVD players and

cordless telephones. The store makes a $75 profit on the sale of each DVD player (d) and a $30 profit on the sale of each cordless telephone (c). The store wants to make a profit of at least $255.00 from its sales of DVD players and cordless phones. Which inequality describes this situation?

a)

$75d+30c<255$

b)

$75d+30c\le255$

c)

$75d+30c>255$

d)

$75d+30c\ge255$

8.

The ninth grade class at a local high school needs to purchase a park permit for $250.00 for their upcoming class picnic. Each ninth grader attending the picnic pays $0.75. Each guest pays $1.25. If 200 ninth graders attend the picnic, which inequality can be used to determine the number of guests, x, needed to cover the cost of the permit?

a)

$0.75x-\left(1.25\right)\left(200\right)\ge\text{250.00}$

b)

$0.75x+\left(1.25\right)\left(200\right)\ge250.00$

c)

$\left(0.75\right)\left(200\right)-1.25x\ge250.00$

d)

$\left(0.75\right)\left(200\right)+1.25x\ge250.00$

9.

The length of a rectangle is 15 and its width is w. The perimeter of the rectangle is, at most, 50. Which inequality can be used to find the longest possible width?

a)

$30+2w<50$

b)

$30+2w\le50$

c)

$30+2w>50$

d)

$30+2w\ge50$

10.

The length of a rectangle is three feet less than twice its width. If x represents the width of the rectangle, in feet, which inequality represents the area of the rectangle that is at most 30 square feet?

a)

$x\left(2x-3\right)\le30$

b)

$x\left(2x-3\right)\ge30$

c)

$x\left(3-2x\right)\le30$

d)

$x\left(3-2x\right)\ge30$

11.

Students in a ninth grade class measured their heights, h, in centimeters. The height of the shortest student was 155 cm, and the height of the tallest student was 190 cm. Which inequality represents the range of heights?

a)

$155<h<190$

b)

$155\le h\le190$

c)

$h\ge155\ or\ h\le190$

d)

$h>155\ or\ h<190$

12.

If five times a number is less than 55, what is the greatest possible integer value of the number?

a)

12

b)

11

c)

10

d)

9

13.

Jason’s part-time job pays him $155 a week. If he has already saved $375, which inequality could be used to determine the minimum number of weeks, w, he needs to work in order to have enough money to buy a dirt bike for $900?

a)

$155+375w\ge900$

b)

$155+375w\le900$

c)

$155w+375\ge900$

d)

$155w+375\le900$

14.

An online music club has a one-time registration fee of $13.95 and charges $0.49 to buy each song. If Emma has $50.00 to join the club and buy songs, which inequality can be used to determine the maximum number of songs, x, she can buy?

a)

$13.95+0.49x\le50$

b)

$13.95+0.49x\ge50$

c)

$13.95-0.49x\le50$

d)

$13.95+0.49x\ge50$

15.

Tamara has a cell phone plan that charges $0.07 per minute plus a monthly fee of $19.00. She budgets $29.50 per month for total cell phone expenses without taxes. Which inequality is used to determine the maximum number of minutes, m, Tamara could use her phone each month in order to stay within her budget?

a)

$19.00-0.07m\ge29.50$

b)

$19.00+0.07m\ge29.50$

c)

$19.00-0.07m\le29.50$

d)

$19.00+0.07m\le29.50$

16.

Which inequality is represented in the graph?

a)

$x<-1$

b)

$x\le-1$

c)

$x>-1$

d)

$x\ge-1$

17.

Which inequality is represented in the graph?

a)

$-4<x<2$

b)

$-4\le x<2$

c)

$-4<x\le2$

d)

$-4\le x\le2$

18.

Which inequality is represented in the graph?

a)

$-3\le x<4$

b)

$-3\le x\le x$

c)

$-3<x<4$

d)

$-3<x\le4$

19.

Which graph represents the solution set of

2x-5<3?

a)

b)

c)

d)

20.

In order to be admitted for a certain ride at an amusement park, a child must be greater than or equal to 36 inches tall and less than 48 inches tall. Which graph represents these conditions?

a)

b)

c)

d)

Modeling Inequalities

Total questions: 20

Worksheet time: 22mins

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