7th Grade Inequalities

Translations

100

You must be at least 50 inches to ride the rise at the amusement park.

 Let x = your height in inches. 

x ≥ 50 

200

Terry can order at most 17 pizzas for the party

t≤17

300

The score, s, must exceed 150 points in order to move to the next round.

s>150

400

8 less than a number, m is less than or equal to 17 

m-8≤17

500

DAILY DOUBLE!!!!!!!!

The sum of twice a number x and 19 is at most 98

2x + 19 ≤ 98

One-Step Inequalities

100

x + 7 < 8

x < 1

200

b - 9 ≥ -20

b ≥ -11

300

4x > 24

x > 6

400

m/3 ≤ 12

m ≤ 36

500

-2x < 18

x > -9

Multi-Step Inequalities

100

3x - 1 ≥ 14

x ≥ 5

200

x/2 - 4 < 10

x < 28

300

9 < 2 - x

-7>x 

x<-7

400

-3 - 6x > -15

 x<2

500

-3(-x-12)≥24

x ≥ -4

Word Problems

100

Kelly is trying to save at least $360 to help her buy a new laptop. Right now, she has $50 and can save $40 per week from this point on. How many weeks will Kelly need to save in order to purchase the printer? 

Write an inequality to represent this situation, with a let statement. Do not solve. 

let w = # of weeks 

50 + 40w ≥ 360

200

Tish earns $450 per week, plus a 4% commission on everything she sells. Write and solve an inequality to find out how much she must sell in order to have a weekly income of at least $800. 

Set up an inequality to solve, with a let statement. Interpret the solution

Let s = how much she sells

450 + 0.04s ≥ 800

s ≥ 8,750

Kelly must sell at least $8,750 worth of stuff. 

300

DAILY DOUBLE!!!!!!!!

George owns a small business and he spent $678 to make wreaths for this holiday season to sell. At least how many wreaths must he sell at $15 each in order to make a profit?

Set up an inequality to solve, with a let statement. Interpret the solution

let w = # of wreaths

15w ≥ 678

w ≥ 45.2

He must sell at least  46 wreaths to make a profit!! 

400

Jenny wants to buy a car. She has $2,000 saved up already for one. She can save about $100 per week. If Jenny wants to save more than $6,000, how many weeks should she save for? 

Set up an inequality to solve, with a let statement. Interpret the solution carefully

let w = # of weeks 

2,000 + 100w > 6,000

w> 40

Jenny will need to save for more than 40 weeks to have enough money. 

500

Zachary went to a carnival and only has $25 to spend. If his ticket to get in was $8, and ride tickets are $1.25 each, what is the maximum number of ride tickets Zachary can buy?

Set up an inequality to solve, with a let statement. Interpret the solution.

let r = # of ride tickets

8+1.25r ≤ 25

r ≤ 13.6 

Zachary can buy at MOST 13 ride tickets.

Miscellaneous

100

Is -5 a solution to the following inequality? 

3m>-20

Yes because -15>-20 is a true statement. 

200

Is 8 a solution to the following inequality?

10+v>18 

no, 18>18 is not a true statement. 

300

Describe what the graph of the solution to the following inequality would look like. 

x -12 < -4

x < 8, closed circle at 8, pointing left

400

Describe what the graph of the solution to the following inequality would look like:

-8x > 32

x < -4, open circle at -4, pointing left

500

How is an inequality different than an equation? Give me your best answer!! 

Ex: inequalities have infinite solutions, equations only have 1 solution.