Chapter 2 Inequalities and Proof Section 2-1 Solving Inequalities in One Variable.
Creating Inequalities in one variable
description
Transcript of Creating Inequalities in one variable
![Page 1: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/1.jpg)
Creating Inequalities in one variable
![Page 2: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/2.jpg)
An inequality is a statement that 2 quantities are not equal. The quantities are compared by using the following signs:
Greater than: > Less than: <Greater than or equal to: ≥ Less than or equal to: ≤
![Page 3: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/3.jpg)
When reading a word problem you need to remember the following:
At most or no more than means “≤”
At least or no less than means “≥”
![Page 4: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/4.jpg)
We will start with creating a basic inequality.
Tom’s dad told him not to turn on the air conditioner unless the temperature is at least 80˚ F.
Turn on the AC when temperature is at least 80˚ Let t represent the temperature.
t ≥ 80˚This is the tricky part…You would probably think that is
supposed to be ≤ BUT at least means that the temperature can be 80˚ or greater than 80˚.
![Page 5: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/5.jpg)
Katy has $650 in a savings account at the beginning of the summer. She wants to have at least $200 in the account by the end of summer. She withdraws $30 each week for food, clothes, and activities. How many weeks can Katy withdraw from her account?
![Page 6: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/6.jpg)
Again at least means greater or equal to.Let w represent the number of weeks.
650 – 30w ≥ 200Start of summer Withdraws 30 each week At least End of summer
650 – 30w ≥ 200-650 -650 - 30w ≥ -450 Divide both sides by a negative 30. Remember to reverse the sign.
W ≤ 15 Katy can withdraw from her account for 15 weeks or less.
![Page 7: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/7.jpg)
An airport shuttle charges a $2.50 flat rate in addition to $0.75 per mile. A couple has no more than $55 to spend on a ride. How many miles can the couple travel without exceeding their limit?
![Page 8: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/8.jpg)
First remember that no more than actually means less than or equal to.Let m represent the number of miles.
.75m + 2.50 ≤ 55.00 - 2.50 ≤ -2.50 .75m ≤ 52.50 Divide both sides by .75 m ≤ 70
The couple can travel 70 miles or less before reaching their limit of $55.
![Page 9: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/9.jpg)
Averages
Jaxon needs at least an 85% to keep his X-Box. His teacher gives 5 tests throughout the semester. His scores were 90, 72, 86, and 94. What score does he need on the fifth test?
![Page 10: Creating Inequalities in one variable](https://reader035.fdocuments.us/reader035/viewer/2022062501/56816301550346895dd3783e/html5/thumbnails/10.jpg)
On a final note……..
*Read through the entire problem*Look for key words that you will need to solve the problem*Identify your variable*Create your inequality*Solve your inequality*Label your answer