Unit 1 A.CED.1 One step Inequalities September 22, 2015

Transcription

1 Answer: Journal Prompt Cristina was working on a multi step problem but she made a mistake. Find the error and explain how she could fix it. 3 x x + 1 = 7x 10 3x 6 + 4x + 4 = 7x 10 x 2 = 7x x = 7x 8 7x 7x 6x = 8 x = 8/ 6 > 4/3 Answer: Journal Prompt When should you use brackets to graph an inequality? When should you use parentheses? Unit 1: A.CED.1 Objective Solve One Step Inequalities Students will be able to create and use inequalities in one variable to represent real world situations and use them to solve problems. You will need to understand inequalities before you can get a driver s license. Look at the picture and write an inequality for the speed limit sign. You are confronted with mathematical inequalities almost every day, but you may not notice them because they are so familiar. Think about the following situations: speed limits on the highway, minimum payments on credit card bills, number of text messages you can send each month from your cell phone, and the amount of time it will take to get from home to school. All of these can be represented as mathematical inequalities. And, in fact, you use mathematical thinking as you consider these situations on a day to day basis. Multiplication Property of Inequality If a, b, and c are real numbers, then a < b and ac < bc are equivalent inequalities. +c When we talk about these situations, we often refer to limits, such as the speed limit is 65 miles per hour or I have a limit of 250 text messages per month. However, n t have to travel at exactly 65 miles per hour on the highway, or send and receive precisely 250 test messages per month the limit only establishes oundary for what is allowable. Thinking about these situations as inequalities provides a fuller picture of what is possible.

2 Vocabulary Inequalities: are mathematical A solution of an inequality is a sentences containing symbols value of the variable that makes the inequality a true statement. Inequalities are used all the time in the world around us we just have to know where to look. Figuring out how to interpret the language of inequalities is an important step toward learning how to solve them in everyday contexts. When you are solving or building these inequalities, it is important to know which inequality symbol you should use. Watch for certain phrases that will tip you off: not equal Is greater than or equal to a < bat most at least Many problems, though, will not explicitly use words like at least or is less than. So how do you figure out which symbol is appropriate in a given situation? The key is to think about the context of the problem, and to relate the context to one of the situations listed in the table. Context refers to the real life situation is which the problem takes place. Bracket End point End Point Summary Parentheses End point [ ] ( ) > < Include > < Don't Include Steps to Solve an Inequality 1. Write the problem 2. Solve the problem as though the inequality sign (<, >) is an equal sign I do 1 x + 1 < 2 3. Decide if the endpoint(s) is racket or parentheses. 4. Graph the solution on a number line using interval notation.

3 2 U Try a a > 24 3 ¼y ½ " at most" Translate Make sure the expenses are no more than $100 I do 4 A number decreased by seven is at most thirteen. U Try A number increased by two is at most six. 5 A number less than five is greater than seven. The sum of a number and fourteen is at least twenty eight.

4 6 An 18 wheel truck stops at a weight station before passing over a bridge. The weight limit on the bridge is 65,000 pounds. The cab (front) of the truck weighs 20,000 pounds, and the trailer (back) of the truck weighs 12,000 pounds when empty. In pounds, how much cargo can the truck carry and still be allowed to cross the bridge? 7 Erykah has found three pairs of running sneakers that she likes, costing $150, $159, and $179. She has saved $31 already, and she has a job where she earns $8.50 per hour. How many hours will she have to work in order to afford any of these sneakers?

5 Attachments Assig 22Unit 1 A.CED.1 One Step Inequalities.docx