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Lesson 22: Problem Solving Linear inequalities

Learn how to construct inequalities to solve real-world mathematical problems step by step. Includes examples and graphing.

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Lesson 22: Problem Solving Linear inequalities

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  1. Lesson 22: Problem Solving Linear inequalities

  2. Essential Question How can you construct inequalities to solve real-world mathematical problems?

  3. Use the same steps as you did for constructing equations!!! • Start with variable • Clue words! • Work around variable • Instead of an equal sign you will need an inequality sign • Solve. Remember GOLDEN RULE! • Include units!

  4. Write the correct inequalityuse c = cost of the tickets1. the cost of 4 tickets is greater than or equal to $20 ____________2. the cost of 4 tickets is at least $20 _________________3. the cost of 4 tickets is at most $20 __________________4. the minimum cost of 4 tickets is $20 ________________5. the maximum cost of 4 tickets is $20 ________________6. the cost of 4 tickets is no more than $20 ______________

  5. 1. Mr. Lin is a telemarketer for a carpet-cleaning service. He is paid $100 per week plus $5 for every customer he brings in. If he wants to make $300 or more this week, how many customers does he need to bring in?

  6. 2. A game show contestant is given $1,000 and then asked 15 trivia questions. For every incorrect answer, the contestant loses $50. How many questions can the contestant get wrong and still take home $700 or more? Solve AND graph the inequality.

  7. 3. Jason is saving up to buy a digital camera that costs $490. So far, he saved $175. He would like to buy the camera 3 weeks from now. What is the inequality used to represent how much he must save every week to have enough money to purchase the camera? Solve the inequality to find an answer.

  8. 4. Walter is buying strawberries and grapes. • The total amount he spends on the fruit must be less than $14.00. • He spends $5.25 on a basket of strawberries. • Grapes cost $1.75 per pound. Write AND graph the inequality to show the values of the amount of grapes Walter can buy.

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