2-Step Inequalities and Word Problems
1. Chris wants to order DVDs over the internet. Each DVD costs $15.99 and shipping for
the entire order is $9.99. Chris has no more than $100 to spend. Write an inequality
that represents Chris’ situation. How many DVDs can Chris order without exceeding
his $100 limit? Justify your answer mathematically.
2. Skate Land charges a $50 flat fee for birthday party rentals and $5.50 for each person.
Joann has no more than $100 to spend on the birthday party. Write an inequality that
represents Joann’s situation. How many people can Joann invite to her birthday party
without exceeding her limit? Justify your answer mathematically.
3. Represent each of the following as an algebraic inequality.
a) x is at most 30
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b) the sum of 5x and 2x is at least 14
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c) the product of x and y is less than or equal to 4
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d) 5 less than a number y is under 20
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4. If 5 times a number is increased by 4, the result is at least 19. Find the least possible
number that satisfies these conditions.
5. The sum of twice a number and 5 is at most 15. What are the possible values for the
number?
6. The cost of a gallon of orange juice is $3.50. What is the maximum number of containers
you can buy for $15?
7. Three times a number increased by 8 is no more than the number decreased by 4. Find the
number.
8. Two-thirds of a number plus 5 is greater than 12. Find the number.