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
Answers
Darcie wants to donate a minimum of blankets.
Will Darcie meet her goal if she crochets.. | Response |
---|---|
Less than blankets? | No |
Exactly blankets? | Yes |
More than blankets? | Yes |
Conclusion | Total blankets |
If Darcie skips days, then she will crochet for days. Darcie crochets at a rate of of a blanket per day, so she can crochet a total of blankets.
This amount must be greater than or equal to blankets, so the inequality is:
To solve the inequality, let's start by multiplying both sides by . Remember that when we multiply an inequality by a negative number, the inequality sign reverses.
Darcie can skip no more than days of crocheting to meet her goal.
To graph the inequality , we first draw a circle at . This circle divides the number line into two sections: one that contains solutions to the inequality and one that does not.
The solution includes the point , so the circle at filled in.
Because the solution to the inequality says that , this means that solutions are numbers to the left of .
The inequality is:
The graph of the solution of the inequality, , looks like this:
2. The inequality is: . The solution set is C: .
Mustafa, Heloise, and Gia have written more than a combined total of articles for the school newspaper.
Is the total number of articles.. | Response |
---|---|
Less than articles? | No |
Exactly articles? | No |
More than articles? | Yes |
Conclusion | Total articles |
Mustafa has written articles. Heloise has written articles. Gia has written articles.
They have written a combined total of articles.
This must be more than articles, so the inequality is:
Let's start by combining like terms.
Mustafa has written more than articles.
The inequality is:
3. The inequality is: . Kim's team scored a minimum of runs per inning.
Kim's team needed more than runs to win.
Would Kim's team win with.. | Response |
---|---|
Less than runs? | No |
Exactly runs? | No |
More than runs? | Yes |
Conclusion | Total runs |
Kim's team already had runs. Since they scored runs per inning for innings, they scored an additional runs, so Kim's team had a total runs.
This must be greater than , so the inequality is:
We can start by subtracting from both sides of the inequality:
Kim's team must score more than runs per inning to win the game. So Kim's team must have scored a minimum of runs per inning.
The inequality is:
Kim's team scored a minimum of runs per inning.
Janey wants to earn enough money to buy a CD for
Can Janey buy the CD if she has.. | Response |
---|---|
Less than ? | No |
Exactly ? | Yes |
More than ? | Yes |
Conclusion | Total dollars |
If Janie does chores, she will earn dollars for doing chores, plus dollars she already has. The amount she has is:
This amount must be greater than or equal to , so the inequality is:
To solve the inequality, let's start by subtracting from both sides of the inequality:
Janie must do or more chores to have enough money to purchase the CD.
To graph the inequality , we first draw a circle at . This circle divides the number line into two sections: one that contains solutions to the inequality and one that does not.
The solution includes the point , so we fill in the circle at .
Because the solution to the inequality says that , this means that solutions are numbers to the right of .
The inequality is:
The graph of the solution of the inequality looks like this: