Lesson 18
Inequalities in Context
- Let’s explore situations that compare values.
18.1: Inequalities
Place a < or > to correctly complete the inequality.
1. 5 \(\underline{\hspace{.5in}} \)10
2. 5 \(\underline{\hspace{.5in}} \) -10
3. -5 \(\underline{\hspace{.5in}} \) -10
4. \(\frac15 \) \(\underline{\hspace{.5in}} \) \(\frac{1}{10}\)
5.\(\frac{-1}{5} \) \(\underline{\hspace{.5in}} \) \(\frac {-1}{10}\)
18.2: Sweater Weather
Elena and Lin are planning some cold-weather camping and are studying jackets and sleeping bags. Here is what they learned about some different equipment.
- A down jacket is rated as comfortable when the temperature is between \(\text{-} 20^\circ\text{F}\) and \(20^\circ\text{F}\).
- A down sleeping bag is rated as comfortable when the temperature is \(\text{-} 20^\circ\text{F}\) or above.
- A synthetic sleeping bag is rated as comfortable when the temperature is \(20^\circ\text{F}\) or above.
![a photo of down jackets hanging in a store](https://cms-im.s3.amazonaws.com/haYaKXppffGPMZqxLGc817fc?response-content-disposition=inline%3B%20filename%3D%22down_jackets.jpg%22%3B%20filename%2A%3DUTF-8%27%27down_jackets.jpg&response-content-type=image%2Fjpeg&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240718%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240718T010939Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5170c319ce8be69ad64e40a70cd0c573b7abc9f26462c7b73e429909f629f1a2)
- What are 2 examples of temperatures that are comfortable for the down jacket?
- For which gear would a temperature of \(\text{-}16.5^\circ\text{F}\) be comfortable?
- Is it possible to list all the temperatures for which the down jacket is comfortable? Explain your reasoning.
- Which item's comfort rating matches each inequality?
- \(x \geq 20\)
- \(\text-20 \leq x\)
- \(\text{-}20 \leq x \) and \(x \leq 20\)
- Here are five graphs of inequalities. Match each graph to a situation in this activity.
A
B
C
D
E
- Are there any temperatures at which the sleeping bags and the jacket would all be comfortable?
- Write one or more inequalities representing the range of temperatures in your area in the winter. Which gear, if any, would you recommend based on that?
18.3: Representing Inequalities
For each statement, write an inequality to represent it. If a variable is used, be prepared to explain what it represents.
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Han has 5 pencils, and Andre has 8.
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Noah has more books than Kiran.
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Clare has more than $200 in her savings account.
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The most the mechanic will charge for an oil change is $60.
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Diego scored 1,200 points in a game, breaking the record for highest score.
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Jada is younger than Tyler.
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Animal World has at least 400 different species of animals.
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Mai’s bowling score is more than Clare’s and Han’s combined.