Two-step Inequalities and Their Applications

This lecture series provides examples of two-step inequalities and their applications. Watch the videos and complete the interactive exercises.

Two-step inequality word problems

1. Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of \frac{1}{15} of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways.

Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.

Graph the solution set to this inequality.


2. Mustafa, Heloise, and Gia have written more than a combined total of 22 articles for the school newspaper. Heloise has written \frac{1}{4} as many articles as Mustafa has. Gia has written \frac {3}{2} as many articles as Mustafa has.

Write an inequality to determine the number of articles, m, Mustafa could have written for the school newspaper.

What is the solution set of the inequality?

Choose 1 answer:

A. m > \frac{1}{2}

B. m \geq \frac{1}{2}

C. m > 8

D. m \geq 8


3. Kim's softball team was playing in the championship game. When there were 4 innings left, the team was losing by a score of 17 to 6 runs. In the last 4 innings, her team scored the same number of runs per inning, and the other team did not score any more runs. Kim's team won with the most runs.

Write an inequality to determine the number of runs per inning, p, Kim's team could have scored.

Find the minimum whole number of runs per inning Kim's team could have scored.


4. Janie has $3. She earns $1.20 for each chore she does and can do fractions of chores. She wants to earn enough money to buy a CD for $13.50.

Write an inequality to determine the number of chores, c, Janie could do to have enough money to buy the CD.

Graph the solution set to this inequality.