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Two-Step Inequalities
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Two-Step Word Problems
100

x -1 > 5

x > 6

100

2x < 4

x < 2

100

9c - 8 ≤ 82

c ≤ 10

100

d > 10.2

What is open circle arrow pointing right (greater than 10.2)

100

Suppose your uncle sends you 5 X-Box games for your birthday. Each game weighs the same amount. The box he mails them in weighs 10 ounces. The total weight of the package is 55 ounces. What is the weight of one game?

What is 9 ounces

200

x + 10 > 10

x > 0

200

7x > 42

x > 6

200

z/3 + 10 > -5

z > -45

200

t ≤ 15.3

What is Closed circle, arrow pointing left (less than 15.3)

200

John & Sue want to buy a DVD player that costs $140. They have $80 saved already. How much will they have to save per month for the next six months in order to have enough money saved?

What is $10

300

x + 5 < 2

x < -3

300

x/8 < 8 

x < 64

300

-18 > -14 + p/8

p < -32

or

-32 > p

300

2x ≥ 12

What is x ≥ 6 Closed circle, arrow pointing right (greater than or equal to 6)

300

The cost of renting a car is $25 per day plus a one-time fee of $75.50 for insurance. Write and solve an inequality to find how many days can the car be rented if the total cost is to be no more than $525.

What is x = number of days 

25x + 75.50 < 525 

x < 17.98 a maximum of 17 days

400

10 > x -12

22 > x

or

x < 22

400

-9x > 81

x < -9

Don't forget to flip your inequaility

400

-8e + 6 ≤ 94

e ≥ -11

Don't forget to flip your inequality

400

5x > 10

What is x > 2 Open Circle, Arrow pointing right (greater than 2)

400

At most, Kyle can spend $50 on sandwiches and chips for a picnic. He already bought chips for $6 and will buy sandwiches that cost$4.50 each. How many sandwiches can he buy?

What is Let x = number of sandwiches 

4.50x + 6 < 50 

x < 9 7/9 a maximum of 9 sandwiches

500

5 < x + 7

-2 < x

or

x > -2

500

-36 > x/-6

216 < x

or

x > 216

Don't forget to flip your inequality

500

8 + 4b ≤ 83

b ≤ 18.75

500

10x - 10 ≤ 90

What is x ≤ 10 Closed circle, arrow pointing left (less than or equal to 10)

500

A bank account has $650 in it. Every week, Sally withdraws $50 to pay for her dog sitter. What is the maximum number of weeks that Sally can withdraw the money so there is at least $75 remaining in the account?

What is Let x = number of weeks 

650 – 50x > 75 

x < 11.5 the maximum is 11 weeks